Experimental and computational study of flapping wing ...

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Experimental and computational study offlapping wing aerodynamics at low reynoldsnumber

Chai, Vincent Wee Sern

2013

Chai, V. W. S. (2013). Experimental and computational study of flapping wing aerodynamicsat low reynolds number. Doctoral thesis, Nanyang Technological University, Singapore.

https://hdl.handle.net/10356/54897

https://doi.org/10.32657/10356/54897

Downloaded on 01 Oct 2021 12:34:06 SGT

EXPERIMENTAL AND COMPUTATIONAL STUDY

OF FLAPPING WING AERODYNAMICS AT LOW

REYNOLDS NUMBER

CHAI WEE SERN VINCENT

SCHOOL OF MECHANICAL AND AEROSPACE

ENGINEERING

2013

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EXPERIMENTAL AND

COMPUTATIONAL STUDY OF

FLAPPING WING AERODYNAMICS AT

LOW REYNOLDS NUMBER

Chai Wee Sern Vincent

School of Mechanical and Aerospace Engineering

A thesis submitted to the Nanyang Technological University in

partial fulfilment of the requirement for the degree of

Doctor of Philosophy

2013

Ch

ai W

.S V

incen

t

I

ABSTRACT

Recent rapid developments in micro-sized Unmanned Aerial Vehicles (UAVs) and

Underwater Vehicles (UWVs) have attracted renewed research interest in flapping

wings aerodynamics. Due to the limitation of the size of these vehicles, complex

motions employed by the birds and fishes have to be simplified as additional

actuators are needed to perform the complex motions which will significantly

increase the size of these vehicles. In addition, the study of flapping wings

aerodynamic is challenging as the parameters involved that affecting the

performance is huge. Therefore, this thesis investigates the feasibility of flapping

wings with simplified kinematic motions as the propulsion system for the micro

UAV or UWV and obtains the optimizing parameters for improving the flapping

wings aerodynamics performance through experimental and numerical simulation

approaches. A simple analytical model for predicting the lift with moderate

accuracy is also developed. In conclusion, with comprehensive works conducted, a

better understanding of the physics behind the flapping wings aerodynamics allows

the translation of knowledge and creates great impact to the development of

flapping wings micro UAV and UWV.

II

ACKNOWLEDGEMENTS Throughout the years of study, the very first person that the author would like to

thanks is his supervisor, Prof. Jorg Uwe Schluter. Although the author transferred

under his supervision only during the final year, Prof. Jorg Uwe Schluter guided

him throughout the project patiently and even not giving up on him when the

author face a series of problems in life during his final year of study. Besides that,

Prof. Jorg Uwe Schluter has helped the author to solve not only financial problem,

also has provided a lot of advises to the author for tackling the difficulty.

The candidate also wishes to express gratitude to his parents and siblings for strong

mental support. Besides that, he would also wish to thanks to Prof Spot, who is his

ex-supervisor, for his great helps during the beginning of his study; he also wish to

take this chance to express his appreciation to Prof Simon Yu, Prof Ooi and Prof

Daniel New for providing thousands of precious advices. The author also treasures

the opportunity that given from the school (Nanyang Technological University) for

offering the research funding and scholarship for his study.

Thirdly, he also likes to the technicians from the University (especially Mr. Eric

Yap, Mr. Nelson and Mr. Seow) for assisting him on this research project. The

candidate also appreciate his lab mate and “blunch kaki” (Ji xiaona, Jerry Xiang,

Airil, Arne, Yu rong, Ernest, Ivan, Kafeng, Imran, John, Abhishek and Sethu) for

constantly giving him support and accompany.

Last but not least, the candidate wishes take this chance to thanks his girlfriend,

Miss Tan Kok Teng, for constant support and understanding during these years.

III

NOMENCLATURE LIST

Roman Symbols

A Vortex Area

A Flapping amplitude

Dimensionless oscillating amplitude

D Diameter

Cdm Mean drag coefficient

Cdo Oscillating drag coefficient

Clm Mean lift coefficient

Clo Oscillating lift coefficient

CL Lift Coefficient

Cp Power Coefficient

Smagorinsky Constant

Dynamic Constant

CT Thrust Coefficient

CFL Courant Friedriches Lewy

CFD Computational Fluid Dynamic

DNS Direct Numerical Simulation

Ε Young Modulus/ Elasticity Modulus

Fx Forces acting at X-Axis of the load cell (Global)

Fy Forces acting at Y-Axis of the load cell (Global)

Fz Forces acting at Z-Axis of the load cell (Global)

I Second moment of inertia

IB Immersed Bounday

J Advance Ratio

K Bending stiffness

LES Large Eddie Simulation

LEV Leading Edge Vortex

P Power generated by oscillating motion of hydrofoil

IV

Pa Pascal

RANS Reynolds-Averaged Navier-stokes

Re Reynolds Numbers

Rechord Reynolds number based on chord length of the foil

SD 7003 Hydrofoil with Selig/Donovan 7003 profile

SD 8020 Hydrofoil with Selig/Donovan 8020 profile

S Surface area of the foil, m2

SGS Sub-Grid Scale

S0 Area of one side of the hydrofoil

St Strouhal Numbers

STS Subtest stress

T Time for one period

TEV Trailing edge vortex

Tx Torque on X-Axis of the load cell (Global)

Ty Torque on Y-Axis of the load cell (Global)

Tz Torque on Z-Axis of the load cell (Global)

V Free stream velocity

Va Speed of advance per unit time

U∞ Free stream velocity

Y Maximum oscillating amplitude

a Plunge amplitude

c Chord Length of hydrofoil

f Oscillating frequency

fx Local force vector in x direction

fy Local force vector in y direction

h (t) Instantaneous heaving Amplitude

k Reduced frequency

t+ Dimensionless time

thold Holding time

uc Combined uncertainty

us Systematic error

V

si Standard deviation

Greek Symbols

ν Kinematic viscosity

Ω Pitch rate

Ω+ Dimensionless pitch rate

ω Vorticity

Γ Circulation

ρ Density of water

η Propulsive Efficiency

σ Normal Stress

ε Strain

Instantaneous pitching angle

Phase angle between the heave and pitch motion

Dynamic viscosity

Turbulent stress tensor

ω Rotational speed

VI

TABLE OF CONTENT

ABSTRACT.......................................................................................................... I

ACKNOWLEDGEMENTS .................................................................................... II

NOMENCLATURE LIST...................................................................................... III

CHAPTER 1 INTRODUCTION .............................................................................. 1

1-1 BACKGROUND ............................................................................................... 1 1-2 OBJECTIVES ................................................................................................... 4 1-3 SCOPE .......................................................................................................... 6

CHAPTER 2 LITERATURE REVIEW ....................................................................... 8

2-1 CONVENTIONAL PROPULSION SYSTEM FOR UAV AND UWV ..................... 8 2-2 EARLY RESEARCH ON FLAPPING WINGS .................................................. 11 2-3 RECENT RESEARCHES OF FLAPPING WING THROUGH FORCE MEASUREMENT ................................................................................................................. 14 2-4 FLOW VISUALIZATION FOR FLAPPING WINGS STUDY ON THRUST AND LIFT

ENHANCEMENT MECHANISM ................................................................................ 24 2-5 THEORETICAL AND NUMERICAL METHODS FOR FLAPPING WING STUDY .. 37 2-6 REMARKS FROM LITERATURE REVIEWS ................................................... 43

CHAPTER 3 EXPERIMENTAL SETUP AND METHOD ........................................... 47

3-1 OVERVIEW .................................................................................................. 47 3-2 WATER TUNNEL ........................................................................................... 47

3.2.1 Water Tunnel Calibration ....................................................................... 48 3-3 FORCE TRANSDUCERS .................................................................................... 54

3-3-1 Force Transducer Suitability Analysis .................................................... 55 3-4 CONSTRUCTION OF THE EXPERIMENTAL TEST RIG FOR FORCE MEASUREMENT .......... 59 3-5 ACTUATION EQUIPMENT ................................................................................ 63 3-6 EXPERIMENTAL PRECAUTIONS AND DATA PROCESSING ........................................ 65 3-7 EXPERIMENTAL ERROR ANALYSIS ..................................................................... 68

CHAPTER 4 COMPUTATIONAL METHOD ......................................................... 71

4-1 OVERVIEW .................................................................................................. 71 4-2 NUMERICAL SIMULATION FOR TURBULENCE FLOW AND LARGE EDDY SIMULATION .... 71 4-3 THE IMMERSED BOUNDARY (IB) METHOD ......................................................... 77 4-4 THE FLOW SOLVER ....................................................................................... 85 4 -5 SIMULATION SETUP AND SUMMARY .................................................................... 86 4-5 GRID INDEPENDENCE TEST ................................................................................... 88

CHAPTER 5 RESULTS AND DISCUSSION ........................................................... 91

5-1 CHAPTER OVERVIEW ..................................................................................... 91 5-2 OSCILLATING CYLINDER ................................................................................. 92

VII

5-3 SYMMETRICALLY HEAVING/OSCILLATING SD8020 AIRFOIL ........................................ 97 5-4 SYMMETRICAL PITCHING OF FLAT PLATE ......................................................... 101

5-4-1 Investigation into the effects of the pitching parameters and free-stream velocity on lift in the symmetrical pitching mode ............................. 102 5-4-2 Image sequence for vorticity plot of pitching flat plate .................... 112 5-4-4 Conclusions on symmetrical pitching plate ......................................... 119

5-5 THRUST INDICATING VORTEX STREET FROM A SYMMETRICAL PITCHING HYDROFOIL .. 122 5-6 THRUST FROM SYMMETRICAL HEAVE AND PITCH SD8020 (IN PHASE AND 180 DEGREES

OUT OF PHASE) ...................................................................................................... 129 5-7 INVESTIGATION OF LEV WITH NON-SYMMETRICAL PITCHING MOTION ................. 135

CHAPTER 6 ANALYTICAL MODEL FOR THE PREDICTION OF PEAK LIFT OF A PITCHING PLATE ............................................................................................ 152

6-1 DERIVATION OF ANALYTICAL MODEL .............................................................. 152 6-2 RESULTS FROM ANALYTICAL MODEL ............................................................... 154 6-3 CONCLUSION OF ANALYTICAL MODEL .............................................................. 159

CHAPTER 7 CONCLUSION AND RECOMMENDATIONS .................................... 160

7.1 SUMMARY .................................................................................................... 160 7.2 RECOMMENDATION AND FUTURE RESEARCH ........................................................ 162

LIST OF REFERENCES ...................................................................................... 164

APPENDIX I LOAD CELL/ FORCE TRANSDUCER DIMENSIONS AND DRAWING .. 171

APPENDIX II ATI CALIBRATION REPORT ....................................................... 172

VIII

LIST OF FIGURES

Figure 1-1 Airfoil performance [2] ..................................................................... 2

Figure 1-2 Animals travel with flapping motion [3], [4] & [5] .......................... 3

Figure 1-3 Humming bird-like miniature UAV (left) and UWV (right) [8] & [9]

........................................................................................................... 5

Figure 2-1 Open rotor and combustion chamber (SGT5-4000F) gas turbine (left)

[10] and Global hawk UAV which uses a gas turbine engine (right) [9] ................. 8

Figure 2-2 Propellers type UAV in smaller size [11] ......................................... 9

Figure 2-3 Micro-Unmanned aerial vehicles (MAV) [12] & [11] ..................... 9

Figure 2-4 Fish-like micro UWV (left) and conventional Type of UWV (right)

[13] & [14] ......................................................................................................... 10

Figure 2-5 Illustration of forces acting on a wing [17] ..................................... 11

Figure 2-6 Illustration of forces acting on a wing (cont.) [17] ......................... 12

Figure 2-7 Dye flow visualization of flapping airfoil [17] ............................... 13

Figure 2-8 D.A. Read experimental test rig in the towing tank [6] .................. 16

Figure 2-9 Foil trajectories for impulsive starting maneuver with 180-degree

pitch change [6] ....................................................................................................... 16

Figure 2-10 Kinematic parameters of the flapping airfoil - relationship between

physical pitch angle and angle of attack [6] ............................................................ 17

Figure 2-11 (a) Kinematical parameters of the airfoil motion and (b) the

definition of the angle of attack α(t) [21] ................................................................ 18

Figure 2-12 Experiment setup from Heathcote’s study [7] ................................ 20

Figure 2-13 Schematic of a flexible airfoil plunging periodically in the vertical

direction [7] ......................................................................................................... 20

Figure 2-14 Variation of thrust coefficient with Reynolds number [7] ............. 22

Figure 2-15 Comparison of propulsive efficiency against other approaches [22] ..

......................................................................................................... 22

Figure 2-16 Illustration on the formation of Kármán Vortex Street ................... 25

Figure 2-17 Flow visualization on Kármán Vortex Street left [26] & right [27] 26

IX

Figure 2-18 Illustration on the formation of reversed Kármán vortex street of jet

flow ......................................................................................................... 27

Figure 2-19 Florescence dye flow visualization on flapping-based propulsion

(top) and asymmetric wake (bottom) [28] .............................................................. 27

Figure 2-20 Dye Flow visualization of vortices behind flapping hydrofoil, Re =

1800, St = 0.29; b/c=4.23x10-3

; a) t/T = 0; b) t/T=1; c) t/T=0.5; d) t/T=0.75. [29] 28

Figure 2-21 Chord-wise flexible wing undergoes heaving motion over a cycle

[22] ......................................................................................................... 29

Figure 2-22 Instantaneous velocity fields at t/T= 0 for Re = 9000, St = 0.56: .... 30

Figure 2-23 Experimental Setup from Willmott’s study [30] ............................ 30

Figure 2-24 Leading and Trailing edge vortex [30] ........................................... 31

Figure 2-25 Flow structure captured at 0.4m/s free stream condition [30] ........ 32

Figure 2-26 Vortex structure and location for bat during down-stroke when wing

is at horizontal with speed of 1 m/s [23] ................................................................. 33

Figure 2-27 Velocity and vorticity fields by DPIV around bat wing in slow

forward flight (1m/s) [23] ....................................................................................... 34

Figure 2-28 Illustration of dynamic stall event for NACA 0012 airfoil [34] ..... 36

Figure 2-29 Sample of overlapping grid [34] ..................................................... 39

Figure 2-30 Comparison of flow structures at different pitch rates by Dye Flow

Visualization and CFD (Vorticity plot) [34] ........................................................... 39

Figure 2-31 Illustration of the airfoil kinematic motion [37] ............................. 40

Figure 2-32 Lift Coefficient time histories of pitching and plunging, and pure

plunging on 2-D flat plate (blue line) and SD7003 (red line) at k = 0.25, λ= 0.6 at

Re = 1 x 104

and 6 x 104, respectively [37] ............................................................. 42

Figure 3-1 Water tunnel .................................................................................... 48

Figure 3-2 Dimensions of water tunnel ............................................................ 49

Figure 3-3 Drawing of DRUCK pressure sensor [39] ...................................... 49

Figure 3-4 Cable connection diagram of the DRUCK pressure sensor [39] .... 50

Figure 3-5 Calibration result of water tunnel by pitot tube .............................. 50

Figure 3-6 Working Principle of Dantec mini-CTA system [40] ..................... 51

Figure 3-7 Location of the CTA probe in the water tunnel test section ........... 52

X

Figure 3-8 Location of calibration plane (distance between measuring points is

for illustration only) ................................................................................................ 52

Figure 3-9 Uniformity and Turbulence intensity across the test section .......... 53

Figure 3-10 Uniformity and Turbulence intensity vertically from the surface to

bottom of the test section ........................................................................................ 54

Figure 3-11 Omega LC-601 force transducer [41] ............................................. 55

Figure 3-12 Omega LC-703 force transducer [41] ............................................. 56

Figure 3-13 OMEGA LC-703 force transducer calibration results .................... 56

Figure 3-14 Force orientation vector on the ATI Force Transducer [42] ........... 57

Figure 3-15 ATI force transducer calibration results (X-axis) ........................... 58

Figure 3-16 Setups for double OMEGA LC-703 force transducer .................... 59

Figure 3-17 Setups for single OMEGA LC-703 force transducer ...................... 60

Figure 3-18 Force diagrams ................................................................................ 61

Figure 3-19 Experimental setups for force measurement by ATI force transducer

......................................................................................................... 62

Figure 3-20 Equipment and test rig for Oscillating test ..................................... 63

Figure 3-21 Experiment setup for heaving and pitching of flat plate and

hydrofoil ......................................................................................................... 64

Figure 3-22 Overview of experiment setup and equipment ............................... 64

Figure 3-23 Natural frequency of the test rig without hydrofoil (a) and with

hydrofoil submerged in the water (b) & FFT from (c) simulation and (d)

experiment and structural frequency test (c) in air and (d) in water ....................... 66

Figure 3-24 Fixture for omega force transducer ................................................. 69

Figure 4-1 An immersed body in the simple Cartesian grid; Ωb as body with

boundary label as Гb and fluid domain Ωf ............................................................... 77

Figure 4-2 Boundary force conditions [52] ...................................................... 80

Figure 4-3 Location of immersed boundary ..................................................... 80

Figure 4-4 Location of Pp and PB [42] .............................................................. 81

Figure 4-5 Simulation setup (masking) ............................................................ 82

Figure 4-6 Pressure boundary conditions ......................................................... 83

XI

Figure 4-7 Time history of pressure drag coefficient for oscillating cylinder on

different grid resolution with fixed time step of 0.002 seconds (left) and different

time step with fixed grid resolution, D/dx = 16 (right). [54] .................................. 84

Figure 4-8 Grid resolution of 320x320x32 ....................................................... 86

Figure 4-9 Lift coefficients versus time plot .................................................... 89

Figure 5-1 Experimental Setup ......................................................................... 94

Figure 5-2 Simulation setup .............................................................................. 94

Figure 5-3 Oscillating Lift Coefficient versus non-dimensional frequency ..... 95

Figure 5-4 Mean and oscillating drag coefficient versus non-dimensional

frequency ......................................................................................................... 96

Figure 5-5 Simulation setup (left) and Truncated trailing edge SD8020 for

numerical simulation (right) [58] ............................................................................ 98

Figure 5-6 Motor rotational frequency for heaving motion of SD8020 ........... 98

Figure 5-7 Lift coefficient (Cl) versus time plot (Simulation and Experiment)

from heaving airfoil with heaving frequencies of (a) f = 0.833Hz, (b) f = 1.083Hz,

(c) f = 1.283Hz and (d) f = 1.5Hz ............................................................................ 99

Figure 5-8 Experimental setup (left) and Numerical setup (right) ................. 101

Figure 5-9 (a) Symmetrical and (b) Non symmetrical pitching up and down

motion ....................................................................................................... 102

Figure 5-10 Time history of phase averaged lift coefficient plots of pitching flat

plate at Reynolds number of 4000 (left column) and 19200 (right column) ........ 105

Figure 5-11 Time history of phase averaged lift coefficient of pitching flat plate

with pitching amplitude of 20 degrees and pitching speed of 100 degree/second at

Reynolds number of 8200, 12240 and 16320 ....................................................... 106

Figure 5-12 Phase averaged lift force of pitching flat plate with α=20 degrees

and 40 degrees to fixed ω = 100 deg/s at Re = 4000 ............................................ 107

Figure 5-13 Phase averaged lift force of a pitching flat plate with pitching

amplitude of 20 degrees and pitching speed of 50 degree/second and 100

degree/second ....................................................................................................... 108

XII

Figure 5-14 Lift curve for pitching flat plate with pitching amplitude of 20

degrees and pitching speed of 50 degree/second to the Reynolds numbers of 4000

and 19200 ....................................................................................................... 109

Figure 5-15 Lift curve for pitching amplitude of 40 degrees and pitching speed

of 100 degree/second with Reynolds number of 4000 and 19200 ........................ 110

Figure 5-16 Lift curve for pitching amplitude of 20 degrees and pitching speed

of 100 degree/second from Re of 4000 to 19200 .................................................. 111

Figure 5-17 Z-component Vorticity plots for Reynolds number of 8200 with

pitching amplitude of 20 deg and rotational speed of 100 deg/s in time sequence ....

115



116



....................................................................................................... 118

Figure 5-20 SD8020 (span width of 0.32m and chord length of 0.12m) with

flexible trailing edge extension ............................................................................. 122

Figure 5-21 SD8020 (a) without and (b) with flexible trailing edge extension for

Dye Flow Visualization at U=0.1028m/s, θ=40o and w=0.873rad/s .................... 124

Figure 5-22 Illustration on the thrust and pitching motions ............................. 126

Figure 5-23 Resultant forces acting on the pitching hydrofoil (a) without and (b)

with flexible extension .......................................................................................... 127

Figure 5-24 Time history thrust with Pitching amplitude: 30deg; Pitching speed:

50deg/s ....................................................................................................... 128

Figure 5-25 Time history thrust with Pitching amplitude: 40deg; Pitching speed:

50deg/s ....................................................................................................... 128

Figure 5-26 Combined heave and pitch motion – in phase .............................. 130

Figure 5-27 Combined heave and pitch motion – 180 degrees out of phase .... 130

Figure 5-28 Experimental setup for combined heave and pitch study ............. 131

Figure 5-29 Time history thrust by combined motion with in phase mode ...... 132

XIII

Figure 5-30 Time history thrust by combined motion with 180 degrees out of

phase mode ....................................................................................................... 133

Figure 5-31 Cross-sectional profile of SD 7003 hydrofoil [58] ....................... 137

Figure 5-32 CAD drawing of SD7003 hydrofoil .............................................. 137

Figure 5-33 Experimental setup ........................................................................ 138

Figure 5-34 Pitch up, hold and pitch down motion .......................................... 138

Figure 5-35 Motion profile of the non-symmetrical pitching motion (Ω+ = 0.2) ..

....................................................................................................... 141

Figure 5-36 Motion profile of the non-symmetrical pitching motion (Ω+ = 1.4) ..

....................................................................................................... 142

Figure 5-37 Lift coefficient Vs dimensionless time with linear sudden motion

profile; a) Ω+ =0.2; hold time 0.072sec (left) and 1.4 sec (right), b) Ω

+ =1.4; hold

time 0.072sec (left) and 1.4 sec (right) ................................................................. 143

Figure 5-38 Lift coefficient Vs dimensionless time with smooth motion profile;

a) Ω+ =0.2; hold time 0.072sec (left) and 1.4 sec (right), b) Ω

+ =1.4; hold time

0.072sec (left) and 1.4 sec (right) ......................................................................... 144

Figure 5-39 Images sequence of smooth pitching (Ω+ = 0.2, hold time of

0.072sec and free-stream velocity of 0.085m/s) for observation of leading edge

vortex (LEV) forming ........................................................................................... 147



vortex (LEV) forming (cont.) ............................................................................... 148

Figure 5-41 Lift and position curve for Ω+ = 0.2, hold time of 0.072sec and free-

stream velocity of 0.085m/s (corresponding to the dye flow visualization) ......... 149

Figure 6-1 Symmetrical pitching motions of flat plate ................................... 155

Figure 6-2 Results from pitching flat plate with pitching parameters of 20 deg 50

deg/s (Left) and 40 deg 100 deg/s (right) with fixed Reynolds number of 19200 155

Figure 6-3 Ilustration of predicted lift components (green dotted line) ......... 157

Figure 6-4 Results from pitching flat plate with fixed pitching parameters (20

degrees and 100 degrees per second) across Reynolds numbers of 8200, 12240,

16320, 19200 ....................................................................................................... 158

XIV

Figure 7-1 Hummingbird micro UAV [68], robotic fish [69] and finger tip size

micro UAV [12] .................................................................................................... 163

XV

LIST OF TABLES

Table 2-1 original and modified SST equation [37] ............................................ 40

Table 2-2 Scope of study ..................................................................................... 46

Table 4-1 Overview of the numerical simulation ................................................ 89

Table 5-1 Pitching parameters and its corresponding Reynolds numbers ........ 103

Table 5-2 Pitching parameters for numerical simulation image sequence ........... 113

Table 5-3 Averaged lift coefficient over entire pitching cycle (Linear sudden

motion) ........................................................................................................... 146

Table 5-4 Averaged lift coefficient over entire pitching cycle (Smooth motion) ...

........................................................................................................... 147

Table 6-1 Pitching parameters and Reynolds number ....................................... 154

Chapter 1 Introduction

1-1 Background

The ability for birds to fly using flapping wings has inspired mankind to dream of

flying. Over the centuries, humans have invented airplanes and rockets in order to

achieve this noble dream. However, the concept of flapping wings has never been

applied on big planes or any flying vehicles as the payload of these vehicles are too

high.

In recent years, unmanned aerial vehicle (UAV) and unmanned underwater vehicle

(UWV) in smaller scale and lower payload have seen unprecedented development

in the military and civilian application. For military purpose, these vehicles are

normally equipped with sensors, GPS module, camera or even weapon [1]. For

civilian application, these vehicles are used mainly for security surveillance or

rescuing purposes. As these vehicles can be controlled without human onboard,

this greatly reduces the risk of injury or even the loss of lives. Thus, these vehicles

can be sent to harsh and dangerous environment which is currently inaccessible by

conventional machines controlled by human pilot.

As discussed above, for UAV or UWV to survive in harsh and dangerous

environment, they have to be more agile, more maneuverable and with a higher

propulsive efficiency to perform more tasks with less energy consumption.

However, the propulsive efficiency of current propeller propulsion method might

already reach stagnation stage. Unfortunately, most of the UAV and UWV in

current days are still using conventional propeller based system for propulsion.

a) Maximum lift coefficient

b) Minimum drag coefficient

c) Maximum lift-drag ratio

Figure 1-1 Airfoil performance [2]

Apart from the factors mentioned above, the micro UAV, which needs to perform

its task in a confined small room, requires to travel in low speed. As fixed wing

vehicles have difficulty in travelling in low Reynolds region due to the maximum

lift coefficient and the maximum lift to drag ratio deteriorated significantly at low

Reynolds number (Figure 1-1), flapping wings vehicles may have the advantages

over fixed wing vehicles for travelling in this slow speed regime. In addition, it

does not occupied large space for containing its big wings or big rotors with the

retractable wings.

Additionally, in the context of underwater vehicles, the propeller based propulsions

vehicles have some critical drawbacks. Firstly, the effect of cavitations and large

scale of turbulence disturbance to the surrounding of ocean lead to high wear and

tear to the blades and the cavitations might generate noises and making it not

suitable for reconnaissance purpose and observing deep sea marine animals.

Secondly, for ocean exploration purposes, rotating propeller blades might be

entangled with marine plants while the vehicle carries out missions in the deep sea.

Figure 1-2 Animals travel with flapping motion [3], [4] & [5]

Hence, by observing the nature, in particular the flapping wings of birds and the

flapping tail of fishes, the flapping wings seem promising in satisfying the

requirements mentioned in previous paragraph. Successful flapping propulsion

might improve the performance of the micro UAV and UWV drastically over those

vehicles equipped with current conventional propulsion system [6] & [7] which

fuels human’s interest in studying the flapping wings again.

Flapping propulsion systems might offer the following advantages: the ability to

generate lift and thrust at the same time, the ability to sustain a higher lift for low

Reynolds number travelling (Figure 1-1), lower noise production in water with

lower flapping frequency, decreased vulnerability to entanglement marine plants

under deep sea environment, and higher agility. With suitable flapping patterns and

parameters, the UAV or UWV can mimic the bird (e.g. the hovering of the

humming bird) or fish to propel itself in narrow or confined area which requires

lower travelling speed and ease of maneuvering.

1-2 Objectives

The performance of flapping wings is determined by many aspects, such as wing

shape, wing motions, wing elasticity, interaction area and et cetera. It is a great

challenge for researchers to examine the factors that influence the performance of

flapping wings aerodynamics which involve the complicated kinematic motions

and the unsteady flow. Hence, in order to develop the micro size UAV or UWV

with great performance, a good prediction tool and set of methodologies to

describe flapping wings aerodynamics is clearly needed. As the complex kinematic

motions require more actuators to perform the required motions and will lead to

increase the size of the micro UAV or UWV, this thesis emphasizes the study of

aerodynamics of hydrofoil or flat plate which undergoes simplified kinematic

motions that include: pure pitching, heaving or combined pitch and heave motion.

With recent improvement in computing power, numerical simulation has becoming

a very popular engineer tool for solving engineering problems more effectively.

However, most of the conventional Computational Fluid Dynamic (CFD) solvers

are difficult to simulate moving object and the preparation job for meshing the

control volume with irregular geometry is tedious. Hence, this thesis evaluated the

accuracy of the Large Eddy Simulation (LES) with Immersed Boundary (IB)

method, as a numerical solver, for simulating the flapping wings aerodynamics.

In summary, this thesis aims to investigate the feasibility of flapping wings with

simplified kinematic motion as propulsion system for micro UAV or UWV through

experiment and numerical simulation, so as to develop a simple analytical model to

predict the lift with moderate accuracy for saving the cost and time from the

engineers to develop and optimizing the performance of the micro vehicles. The

study of flapping wings aerodynamics also aims to investigate the existence of the

lift and thrust enhancement mechanisms which could be utilized in the flapping

wings micro vehicles for optimizing its propulsion performance.

Figure 1-3 Humming bird-like miniature UAV (left) and UWV (right) [8]

& [9]

1-3 Scope

One of the main challenges in the study of flapping wings is the measurement of

relatively small forces generated by the flapping wings. The main scope of this

research is described as below:

1. The development and validation of an experimental setup which is capable

of generating wing motions and accurately measuring the small flapping

forces.

2. The validation of the computational results with the experimental results

obtained in order to evaluate the suitability of the numerical solver for the

flapping wings study.

3. The derivation and provision of design recommendations of flapping wings

for UAVs and UWVs as propulsion system.

The flapping parameters under investigation in this study are:

1. Type of Motion : Symmetrical and non-symmetrical heaving, pitching

and combined motion.

2. Speed : Heaving and pitching speed.

3. Amplitude : Heaving and pitching amplitude.

Lastly, the outline of this thesis is:

Chapter 1 provides a brief introduction and background of flapping wings

aerodynamics as well as to highlight the objectives and the scopes of study.

Chapter 2 discusses the literature reviews on past researches for the study of

flapping wings and the evolution of the conventional type of the propulsion system

for the UAV and UWV.

Chapter 3 presents the design and development of the test rig, the selection of the

tools as well as the error analysis for the equipment used throughout the study.

Chapter 4 introduces the numerical solver, the Large Eddy Simulation (LES) with

the Immersed Boundary (IB) method and the discussion on the selection of

turbulence models and the solver.

Chapter 5 highlights and discusses the experimental and numerical simulation

results obtained from:

Oscillating cylinder test,

Flapping hydrofoil or flat plate with different combination of flapping

parameters and Reynolds number involved,

Study on the effect of flexibility of hydrofoil,

Study on the lift and thrust enhancement mechanism.

Chapter 6 concludes the research conducted and contributions of the thesis. This

chapter also highlights the potential areas for future studies on flapping wings

aerodynamics for the development and optimization of micro UAV and UWV

propulsion system.

Chapter 2 Literature Review

2-1 Conventional propulsion system for UAV and UWV

In current day, with the heavily needs of air transport, gas turbine engine has

becoming very popular for airplane as propulsion system. The first patent for gas

turbine development was issued to John Barber (1791) [10].

Many decades later, Hans J.P von Ohain (1935) has developed a gas turbine power

plant, which consists of a multistage axial flow compressor and turbine on the same

shaft with a combustion chamber and a heat exchanger for Heinkel aircraft in

Germany and flied successfully [10].

During the year 1950, the development of gas turbine technology for aircrafts

power plants was having vast improvement. In modern days, many new engines

were developed in twentieth century by Rolls Royce, General Electric and Pratt and

Whitney.

Figure 2-1 Open rotor and combustion chamber (SGT5-4000F) gas turbine

(left) [10] and Global hawk UAV which uses a gas turbine

engine (right) [9]

Figure 2-2 Propellers type UAV in smaller size [11]

Owing to the mature developments of gas turbine engine, it has been employed for

larger UAV (Figure 2-1, right). Besides gas turbine engine, some of the smaller

UAV, which does not require traveling fast and lesser payload, uses propeller type

of propulsion system (Figure 2-2). However, for micro-size unmanned vehicle,

fixed wing propeller type UAV has limitation in operation at low Reynolds number

(Figure 1-1). Therefore, different types of propulsion system have been invented.

Figure 2-3 shows micro UAVs which use flapping wings and quad-rotor

propulsion system.

Figure 2-3 Micro-Unmanned aerial vehicles (MAV) [12] & [11]

The quad-rotor type UAVs (Figure 2-3, right) might have better maneuverability

than fixed wings vehicle, but it requires a large space for accommodating its rotors

where flapping wings type UAVs do not (Figure 2-3, left).

Similarly, for the UWV, fish liked flapping tails allow the vehicle to be further

reduced in size and improve the maneuverability. Figure 2-4 shows the

conventional type of underwater vehicle which is equip with conventional type of

propulsion system (right) and fish-like underwater vehicle with flapping tail (left).

Figure 2-4 Fish-like micro UWV (left) and conventional Type of UWV

(right) [13] & [14]

Apart from factors mentioned above, the propulsive efficiency is also noteworthy

for the operation of micro UAV and UVW. According to Jamie Marie Anderson

[15], the highest thrust in all propulsors is produced at low advance ratio where the

efficiency is near zero; and the highest efficiency occurs when the thrust coefficient

is reduced by about 50%. Hence, it is not practical to operate large propellers at

low frequencies while a large motor is needed. Furthermore, according to simple

actuator disk theory [15], the efficiency is trading off from the thrust coefficient as

the thrust is increased. Therefore, flapping type of propulsion system can act as

competitors to conventional propellers.

The advance ratio of the propeller can be defined as the following equation:

(2-1)

where, Va is the speed of advance per unit time, n is the propeller’s rotational speed

(revolutions per unit of time) and D is the propeller’s diameter. [16]

2-2 Early Research on Flapping Wings

The early explanation of a bird’s ability to produce thrust and lift by its flapping

wings was published by Knoller (1909), followed by Vienna and Betz (1912) in

Göttingen [17]. They found that, at low angles of incidence to the incoming flow, a

lift force on a stationary aerofoil in free-stream almost normal to the incoming flow

will be generated. If the drag on the wing is small compared to the lift, the resultant

force is normal to the incident flow as well. Illustration is shown in Figure 2-5.

Figure 2-5 Illustration of forces acting on a wing [17]

As opposed to the case mentioned above, the oscillating airfoil with a heaving

motion (moving up and down with a fixed angle of attack) sees an induced vertical

velocity causes an incoming velocity with an angle of incidence to the real free

stream direction as shown in Figure 2-6.

Figure 2-6 Illustration of forces acting on a wing (cont.) [17]

Next, Knoller and Betz conducted further research and found that if the wing is

being oscillated in a heaving motion, the lift force will be both positive and

negative in a cycle. However, its thrust force would always be a non negative value

even though the averaged-lift is zero. In 1922, Katzmayr conducted the first wind

tunnel test on an airfoil that was mounted in an oscillating free stream and

concluded that the airfoil was experiencing a thrust force.

In addition, Katzmayr concluded that the flapping wings, together with appropriate

flapping parameter, can generate thrust whenever the airfoil changes its angle of

attack. At the same time, the flapping airfoil can continuously shed vortices from

its trailing edge, similar to jet flow pattern (Figure 2-7) which is also known as

Reverse Karman Vortex Street. In 1924, Prandtl’s student, Birnbaum [17]

presented a theoretical solution for the incompressible flow over flapping foils.

Apart from the pure oscillating motion, recent developments and research on

flapping wing have focused on the motion of flying birds or insects and swimming

fishes.

Due to the complex motion of flapping wings, besides the capability of generating

thrust, in 1932, Kramer [18] first demonstrated that a wing can experience lift

above the stall value when the wing is flapping from low to high angle of attacks

and experience rapid wing rotation at the ends of the down-stroke and up-stroke

from insect flight. This motion of flapping wings allows introducing circulation

into the flow and it is known as the Kramer effect. Hence, the rapid rotation

(Kramer effect), acceleration of the flapping wings (Wagner effects [19]) and the

LEV - lift enhancement mechanism allows the flapping wings to enhance the lift

for insect flight.

Figure 2-7 Dye flow visualization of flapping airfoil [17]

2-3 Recent researches of flapping wing through Force measurement

Throughout the flapping wings studies in recent years, most of the researchers

focused on investigating the thrust or lift performance and the propulsive efficiency

of the flapping wings. Before reviewing the researches done on flapping wings,

some of the common parameters that were applied across the studies of flapping

wings among researchers are introduced in the beginning of this section. The

Strouhal number is a dimensionless value that describes the phenomenon of

oscillating flow (e.g. Oscillating hydrofoil for flapping wings study):

(2-2)

where h0 is the heave amplitude, ω is the circular frequency in rad/s and U is the

velocity.

The average thrust force (x-direction) obtained from the force measurement is

defined as:

; For

(2-3)

The mechanical power delivered by the motors for the motion is defined as:

(2-4)

where Fy is the force experienced in y-direction and th is the heaving speed, Q(t)

is the torque in the XY plane and t is the angular velocity in the Z axis.

The thrust and power coefficients are:

(2-5)

(2-6)

Lastly, the propulsive efficiency is:

(2-7)

In recent years, due to the advancement in technology, the measurement of the

thrust and lift forces that the flapping wing has becoming more feasible and more

accurate. However, the actuation mechanism, force measuring sensors, the other

relevant equipment and environment for conducting the experiment are still

amongst the greatest challenge in the experimental setup in order to obtained more

accurate results.

D.A. Read [6] conducted a series of experiments (Figure 2-8) to study the

performance of the oscillating foil with simple profile (NACA 0012) with a huge

carriage in a towing tank at the Reynolds number of 4000 to investigate the

relationship between the oscillating simple foil (Figure 2-9) and its propulsion and

maneuvering ability. The chord length of the foil is 10 cm and span-width of 60 cm.

The classical oscillatory thin airfoil theory [17] states that the propulsive efficiency

of a single heaving airfoil in slow oscillatory motion is only about 50%. Therefore,

it requires a large airfoil to sustain the thrust value significantly. However, from the

D.A. Read study, a maximum propulsive efficiency of 71.5% was archived at αmax

= 15º, ψ = 90 º and St = 0.1.

Figure 2-8 D.A. Read experimental test rig in the towing tank [6]

Figure 2-9 Foil trajectories for impulsive starting maneuver with 180-

degree pitch change [6]

From Figure 2-10, the heave h(t) and pitch θ(t) amplitude are defined as:

(2-8)

(2-9)

is the phase angle between the heave and pitch motion and the resulting angle of

attack profile are defined below (all angles are measured in radians):

(2-10)

Figure 2-10 Kinematic parameters of the flapping airfoil - relationship

between physical pitch angle and angle of attack [6]

In 2007, Liu [20] studied the effects of oncoming flow unsteadiness on the

aerodynamic characteristics of the flapping wings. When the wing altering its angle

of attacks, the flow separation occurs in the vicinity of the leading edge at moderate

angles of attack, however, quasi-steady aerodynamics analysis is unable to predict

these phenomenons and hence, it is necessary to use the Navier stokes equation

with suitable turbulence models in order to obtain accurate and quantitative results.

Therefore, Liu further investigated the effects that were mentioned above by

conducting a series of experiments in a towing tank. The hydrofoil was undergoing

heave and pitch oscillations about the quarter-chord point. His results show that the

thrust and the efficiency of the wing propulsors decreased with an increasing mean

angle of attack. Furthermore, high efficiency can be achieved for operation at

angles of attack close to those of maximum lift-to-drag ratio.

In 2005, Schouveiler [21] conducted a study on the performance of aquatic

propulsion system, which was inspired from the uniform swimming mode with the

combination of pitching and heaving by the hydrofoil NACA0012 (Figure 2-11,

chord length of 0.1m). The experiment was conducted with a fixed Reynolds

number (Rechord = 40,000). A peak efficiency of more than 70% was obtained.

Figure 2-11 (a) Kinematical parameters of the airfoil motion and (b) the

definition of the angle of attack α(t) [21]

Heathcote [7] also conducted a series of experiments for investigating the effects of

the elasticity of a flapping hydrofoil under pure heaving motion to the lift and

thrust. However, conducting such experiments in the towing tank has its limitations,

such as, the available travelling distance. Besides that, the size of travelling

carriage is huge and complicated. Therefore, Heathcote used a water tunnel instead

of the tow tank. The experimental setup is shown in Figure 2-12.

The experiments were first conducted in the water tunnel with stationary water for

avoiding the disturbance from free-stream. Then, it was repeated with the incoming

flow within the Reynolds number from 9000 to 27000, for investigating the effects

of Reynolds to the flapping performance.

Figure 2-12 Experiment setup from Heathcote’s study [7]

Figure 2-13 Schematic of a flexible airfoil plunging periodically in the

vertical direction [7]

Heathcote stated that the deformation of the flexible airfoils could produce an

imaginary angle of attack that varies periodically with the phase angle. The

deformation of the flexible airfoils which respects to the pure heaving motion is

indirectly acting as the combination of heaving and pitching motion with certain

heaving amplitude and phase angle between the imaginary pitching motions.

Figure 2-13 illustrates the heaving motion and the flexible section of the airfoil; the

displacement of the trailing edge is denoted by STE (t). The leading edge is plunged

sinusoidally (SLE) with plunge amplitude a, frequency f and c is the chord length.

The free stream velocity is zero for the first run set of experiment, U∞ = 0 m/s.

The three dimensionless parameters are:

h = a/c, (2-11)

Re = f c2/ν, (2-12)

K = I/μνc (2-13)

Where I = Eb3/12 (second moment of inertia). h is dimensionless parameter for the

ratio of plunge amplitude to chord, Re is Reynolds number, f is the plunge

frequency, is the dynamic viscosity, ν is the kinematic viscosity and K is the

bending stiffness of the plate k.

Figure 2-14 Variation of thrust coefficient with Reynolds number [7]

Figure 2-15 Comparison of propulsive efficiency against other approaches

[22]

From Figure 2-14, the very flexible hydrofoil has the highest thrust coefficient at

Reynolds number of 9000, but it decreased to the least at Reynolds number of

20000. However, the very flexible hydrofoil can achieve the highest thrust to

power ratio among the rest of the hydrofoil.

In addition, Figure 2-15 shows that the highest propulsive efficiency that the

heaving hydrofoil can attain is at the Strouhal number of 0.1 and the propulsive

efficiency is deteriorated at high Strouhal number.

Lastly, Heathcote concluded that, good control on the degree of flexibility at the

trailing edge could improve the thrust performance and the propulsive efficiency.

However, due to pure pitching motion can produce higher thrust as compare to

pure heaving flapping motion [6] & [21], a similar test with pure pitching instead

of heaving motion, with the flexible trailing edge, will be conducted for current

study.

2-4 Flow visualization for Flapping Wings study on thrust and lift

enhancement mechanism

As fluid flows are almost invisible to human’s eyes, flow visualization needs to be

performed in order to allow the flow pattern to be visible to us. The interaction

between the flapping wings to the fluid and the creation and shedding of vortices

from the flapping wings is important for the performance of lift and thrust

generated by the flapping wing. As a result, conducting flow visualization enables

us to obtain more information from flapping wings.

The most frequently used flow visualization technique is the dye flow visualization;

however this technique can only provide very basic information which regarding

the flow structure. With the advancement of technology, more information such as

the velocity vector, magnitude and vorticity of the fluid flows can be obtained.

Particle Image Velocimetry (PIV) is another new method that has been frequently

utilized for fluid study in current day. Besides that, accurate CFD simulation also

allows us to obtain the relevant information.

The main purpose for performing flow visualization is to reveal the hidden physics

behind as well as to observe the vortices and the shedding vortex structure from

flapping wings, for example thrust indicating Reversed Kármán vortex street. Its

appearance can be further validated by the results obtained from the force

measurement. Besides that, the interaction of the leading edge vortex to the

flapping wings is also vital for optimizing flapping wings performance. The four

major lift-enhancement mechanisms in flapping wings aerodynamics are [23]:

Delayed stall due to Lead-Edge Vortices (LEV)

Aerodynamic peak due to pitch-up rotation

Wake capture due to vortical flow and airfoil interactions

Weis-Fogh’s clap and fling dynamics

Vortex shedding [24] occurs when pressure differences arise [25]. Figure 2-16

shows that, when the pressure at P2 is lower than P1, the flow curls inwards and

causes the upper and lower vortex to rotate clockwise and counter clockwise

respectively. The detachment and shedding of the vortices at the downstream is

normally known as the Kármán vortex street and it usually occurs if an object is

experiencing drag [2].

The shedding of vortices will cause the object becomes unstable. Construction

engineers should not design a building with a natural frequency which is close to

its shedding frequency so as to prevent catastrophe (e.g. the collapse of Tacoma

Bridge).

Figure 2-16 Illustration on the formation of Kármán Vortex Street

Figure 2-17 Flow visualization on Kármán Vortex Street left [26] & right [27]

Figures 2-17 (a) and (b) shows the Kármán vortex street with an unsteady periodic

behaviour flow pattern over a bluff body. Figure 2-17 (b) shows the flow passing a

cylinder with a diameter of 6.35 mm at Reynolds number of 168 (captured by the

hydrogen bubble flow visualization technique). From this figure, the Kármán

vortex street can by identified by its “mushroom head” which is always pointed to

the upstream.

Its reverse phenomenon, the reverse Kármán vortex street, can be observed at the

downstream of bird flapping wings, swimming fish and jet flow [2]. Figure 2-18

illustrates the flow interaction between the jet and the free-stream. The flow is

being ejected directly from the jet, pushes the surrounding fluid away and causes

the upper and bottom vortex to rotate counter-clockwise and clockwise respectively.

Figure 2-19 shows the reverse Kármán vortex street which was captured from the

florescence dye flow visualization conducted on flapping hydrofoil. The method

for identifying the reverse Kármán vortex street is shown in Figure 2-19, where the

direction of the “mushroom head” is pointing to the downstream.

a) b)

Figure 2-18 Illustration on the formation of reversed Kármán vortex street

of jet flow

Figure 2-19 Florescence dye flow visualization on flapping-based propulsion

(top) and asymmetric wake (bottom) [28]

Apart from the force measurement which mentioned in the previous section,

Heathcote [22] has also performed a series of flow visualization, with both dye

flow visualization and PIV technique, for observing the flow structure pattern at

the down-stream of flapping elastic wing. Figure 2-20 illustrates the flow pattern at

the downstream of heaving hydrofoil; the reverse Kármán vortex street can also be

clearly seen. The images sequence from Figure 2-21 was captured by the PIV

which shows the motion and the deformation of the elastic wing over a cycle. The

PIV technique allows obtaining the velocity vector field around the heaving

hydrofoil and the strength of vortices can be further derived. Hence, from his study,

the flow structures from the heaving hydrofoil in different stiffness were

distinguished.

Figure 2-20 Dye Flow visualization of vortices behind flapping hydrofoil, Re

= 1800, St = 0.29; b/c=4.23x10-3

; a) t/T = 0; b) t/T=1; c) t/T=0.5; d) t/T=0.75. [29]

Figure 2-21 Chord-wise flexible wing undergoes heaving motion over a cycle

[22]

Figure 2-22 Instantaneous velocity fields at t/T= 0 for Re = 9000, St = 0.56:

a) b/c = 4.23 x10-3

; (b) b/c = 1.41 x 10-3

; (c) b/c = 0.56 x 10-3

. [22]

In 1997, Willmott P.A. [30] conducted an experiment on hawk moth (insect flight)

to investigate the aerodynamic mechanisms (e.g. Leading Edge Vortex and etc)

which is employed during the flight of the hawk moth. The experimental setup with

hawk moth for flow visualization test is illustrated in the figure below:

Figure 2-23 Experimental Setup from Willmott’s study [30]

A vertical streamlined smoke rake was placed on the centre line of the wind tunnel,

upstream of the contraction area. A camera was used to capture the image, while

illumination was provided by four strobe lamps, which was positioned to provide

maximum contrast between the smoke and the black background as shown in

Figure 2-23 to capture a clear image.

The flight speed was simulated as the flow passing through the moth with the speed

varying from 0.4 to 5.7m/s. The captured wake consists of an alternating series of

horizontal and vertical vortex rings which were generated by the successive down

and up strokes. Most importantly, it has proved the ability of down stroke for

producing significantly more lift than the up stroke with the appearance of LEV.

The leading edge vortex (LEV) grew in size with increasing forward velocity and it

acted as a mechanism for enhancing lift for many insects. A small jet provides

some additional thrust as the trailing edges approach the end of upstroke.

Figure 2-24 Leading and Trailing edge vortex [30]

When the wings are in late supination (the action of wings rotation where the

bottom part of the wings are facing upward), a leading edge bubble on the ventral

surface of the wings appears in Figure 2-24b. This bubble is consistent with a flex

mechanism for creation of circulation during isolated rotation and the circulation

remained attached to the wing, and therefore the lift is enhanced during the

subsequent translation. The photo sequence from the conducted flow visualization

is shown in Figure 2-25.

Figure 2-25 Flow structure captured at 0.4m/s free stream condition [30]

Next, F.T Muijres [23] conducted flow visualization and PIV test on the bat flight

in order to investigate the effect of lift enhancement mechanisms. He found that the

LEV helped to increase the lift by 40% on the bat, which is a heavier and larger

animal as compared to insects.

Figure 2-26 Vortex structure and location for bat during down-stroke when

wing is at horizontal with speed of 1 m/s [23]

The structures and location of various vortices are illustrated in Figure 2-26. There

are two closed loops vortices where one is over the left and the other is over the

right of the wing. The loop is connected to the start vortex and shed in the wake via

the tip vortex and the root vortex, where the yellow-zone indicates low circulation

and the red-zone constitutes high circulation. Figure 2-27 shows the LEV obtained

from the DPIV conducted on the bat wing (in different chord-wise direction). Since

LEV vortex is a type of lift enhancement mechanism which is proven to be existed

in animal flight from the researches mentioned earlier. In this thesis, the flow

visualization technique and direct force measurement were applied with

synchronized timing for observing the forming and bursting of the LEV and

investigating the performance of the lift by examine the hydrofoil which underwent

simplified flapping motion quantitatively (focusing on the 2-D motion).

Figure 2-27 Velocity and vorticity fields by DPIV around bat wing in slow

forward flight (1m/s) [23]

From the previous reviews of flow visualization on insects and flying animals,

existence of LEV from the animals’ flight is proven to affect the lift performance

significantly. Next, the dynamic stall or delayed stall [31], which is a type of

unsteady aerodynamics effect, is widely known as one of the important factors that

greatly affect the performance of the unsteady lift generation. Hence, this section

explained the dynamic stall effect. This effect occurs when the foil changes its

angle of attack rapidly [32], forming a strong vortex which sheds from the leading

edge of the aerofoil and travels to the back of the wing top. Lift is increased if this

particular vortex sheet, which contains high velocity flow, travels above the airfoil;

after the flow passes the trailing edge, the lift reduces abruptly and returns back to

its normal stall.

The dynamic stall can normally be found in helicopters and flapping flights [33].

For a helicopter in forward flight, the angle of attack changes rapidly when the

helicopter blade is in the reverse direction to the incoming flow. However, for

flapping flights, such as that of an insect, it may rely on dynamic stall to produce

lift if the flapping motion is fast enough [34].

As mentioned, the flow reversal above the airfoil will affect the pressure

distribution after the wing rapidly exceeds the static stall angle (Point (b) of Figure

2-28). Subsequently, this reversal progresses up on the upper surface of the airfoil

and forms a vortex, initially at the leading edge of the airfoil (Point (e) of Figure

2-28), but which is later enlarged and moved down to the airfoil.

When the pitching moment reaches its negative peak, both lift and pitching

momentum start to drop (point h & i) and dynamic stall occurs. As the angle of

attack decreases, the vortex sheds into the wake and a fully separated flow

develops on the airfoil. When the angle of attack reaches its minimum, the lift does

not reach its minimum, indicating that the dynamic stall process has formed a

hysteresis loop.

Figure 2-28 Illustration of dynamic stall event for NACA 0012 airfoil [34]

2-5 Theoretical and numerical methods for Flapping Wing study

Oi [35] has investigated the effect of dynamic stall through experiments, numerical

simulation and dye flow visualization, to create a simple model, by modified the

Theodorsen’s equation with a simple attached flow model, for predicting lift in

time history for a wide range of kinematics motion in order to benefit the

engineering purposes with reasonable accuracy.

The modified model considered the following parameters which include the

reduced frequency, flapping amplitude, Reynolds number and etc. As such, the lift

coefficient from the modified Theodorsen’s model can be represented by:

(2-14)

The pitch and plunge are input as complex exponentials,

(2-15)

The phase lead of pitch to plunge, in the fraction of motion period is , reduced

frequency is represented by2

ck

U

. The first term measures the steady lift, the

second term is the “apparent mass” or non-circulatory lift due to acceleration effect

and the third term models the circulatory effect. C(k) is the complex valued

“Theodorsen’s function” with magnitude less than one. It is a transfer function

accounting for the lift amplitude and the phase lag response from its real and

imaginary parts respectively. The assumption is based on the equation which

considers only on a planar wake and a trailing edge Kutta condition; therefore, it

does not consider the wake rollup, vortex street, vortex shedding, convection of

large separations over the airfoil, large laminar separation bubbles, leading edge

and trailing edge vortices. However, Theodorsen’s prediction and computation is

not worsening in the deep stall (plunge only) as compared to the shallow stall

(pitch-plunge). He suggested that the LEV formation and the reversed flow region

above the suction side are not principal contributors to lift coefficient.

Lian [34] has conducted a numerical study on the pitching flat plate at low

Reynolds number by unsteady, incompressible and laminar flow model (Figure

2-29). The investigation on the effect of pitch rate, Reynolds number, and location

of pitch axis as well as the computational grid size were conducted and compared

with the experimental results. He has found that increasing pitch rate allows the

LEV to be more compact and stronger; secondly, moving the pitch position further

from the leading edge will weaken the LEV on the top surface when the plate is

pitching upward. As the pitch position passes the middle of the chord, the vortex

appeared at the bottom surface, where it is believed to be caused by the effective

angle of attack. The influence of the Reynolds number on the flow structure is

depended on the pitch rate; the effect of Reynolds number is strong when the pitch

rate is low; however, its effect is weak when the pitch rate is high. In addition, the

computational grid size will also affect the results of the calculated aerodynamic

forces; a smaller grid increases the lift generation value when the plate is pitched

up.

Figure 2-29 Sample of overlapping grid [34]

Figure 2-30 Comparison of flow structures at different pitch rates by Dye

Flow Visualization and CFD (Vorticity plot) [34]

Liu [20] stated that the quasi-static inviscid flow analysis is not accurate for

modeling flapping wings aerodynamics. Hence, it is necessary to use the Navier-

Stokes equation with a suitable turbulence model instead of laminar model. His

statement is in contrast to Lian as the laminar model is not accurate for modeling

the vortices. However, in recent year (2011), Patrick [36] has conducted a

numerical simulation for studying the hovering of rigid flapping wing

aerodynamics by laminar flow model. He explained that, extensive numerical study

based on complicated turbulence model is very time consuming and expensive.

Kang [37] conducted a simulation with original Menter’s Shear Stress Transport

(SST) turbulence model on rigid flat plate and SD7003 hydrofoil which undergoes

pitching and plunging motion (2D condition). The governing equations used are

RANS equations coupled with Menter’s SST model and the continuity equation for

incompressible flow. However, Menter’s original SST turbulence model has a limit

on the production term. Therefore, Kang modified the main equation in order to

obtain a more accurate result. The modified equations are shown in the table below:

Table 2-1 original and modified SST equation [37]

Figure 2-31 Illustration of the airfoil kinematic motion [37]

Figure 2-31 illustrates the heaving and pitching motion of the airfoil. The equations

below explain the relationship between the motion, time and the free-stream

condition.

(2-16)

(2-17)

(2-18)

h is the location of the center of rotation ( / 0.25)px c from the leading edge; 0h is

the normalized plunging amplitude, c is the chord length of the airfoil; 0 is the

mean angle of attack and A is the amplitude of the pitching motion.

The effective angle of attack is represented by e ; which is a linear combination of

the pitching angle and the induced angle due to plunging motion. St is the Strouhal

number and is ratio of the maximum effective angles of attack of the pitching

motion to the plunging motion and h is the plunge-velocity, k is the reduced

frequency.

Figure 2-32 Lift Coefficient time histories of pitching and plunging, and

pure plunging on 2-D flat plate (blue line) and SD7003 (red line) at k = 0.25,

λ= 0.6 at Re = 1 x 104

and 6 x 104, respectively [37]

Kang concluded that the modified SST turbulence model over-predicts the flow

separation. For the simulation on flat plate, the leading edge effects overwhelmed

the difference between turbulence models. Therefore, Kang concluded, for the flow

over flat plate, in all numerical simulation approaches, the geometrical effect at

sharp leading edge is the dominating factor for triggering the separation from the

leading edge for both pitching and plunging motion and causes the instability of the

simulation. Hence, Guerrero [38] employed the overlapping grids method for

tackling the problems of sharp edged geometry by overlapping the refined grid

around the flapping hydrofoil.

2-6 Remarks from Literature Reviews

The above literature studies examined within this chapter have led the author to

conduct further investigations on flapping wings aerodynamics as there is still a

huge gap for the improvement; either in the field of numerical study or to optimize

the performance of the flapping wings aerodynamics as the parameters that

involved for flapping flight is very large. Apart from that, various approaches

adopted by different researchers to obtain useful data which mentioned in this

chapter have provided the author a clearer picture to develop the experimental test

rig, the numerical model and a simple analytical model. Hence, this thesis will

focus on the followings areas:

1. Experimental

The fish swimming and bird flying motion can be simplified as heaving, pitching

or combined heave and pitch motions. With these simplified motions, the amount

of actuators, which are needed to perform complex motions, can be reduced; hence,

the size of these micro-vehicles can also be minimized. However, in order to

investigate the capability of these simplified motion for producing lift and thrust, a

test rig, which has the capability for conducting the above mentioned tasks with

low measurement uncertainty, has to be developed. Apart from that, size of test rig,

ease of operation, repeatability, flow quality and accuracy of measuring tool are

also act as important factors for building a good test rig. From the literature study,

it is found that towing tank has its limitation on the travel distance; the

corresponding test rig has to be movable and the design of the carriage is huge and

complicated.

Hence, due to the above mentioned factors, this thesis will utilize a close-loop

water tunnel with a simple test rig for conducting the force measurement and dye

flow visualization. Chapter 3 discusses the details on the selection of equipment,

the design and development of the test rig, as well as error analysis.

2. Numerical simulation and simple mathematical model

Some researchers stated that quasi-static stage of approximation, laminar and

RANS turbulence model are not able to accurately predict the flapping

aerodynamics properties due to the unsteadiness of flow involved. In order to

predict the unsteady mechanism mentioned, a correct turbulence model has to be

employed in order to portray the aerodynamics performance of flapping wings.

However, time and cost for conducting extensive numerical simulation based on

higher accuracy turbulence model or Direct Numerical Simulation (DNS) are

always a factor that halting researchers to implement it. Apart from that, the

conventional CFD solvers which utilized body fitted method are having difficulty

on meshing complex geometry. The pre-simulation stage for moving object is also

very tedious and the co-ordinate mapping is required in order to perform the

calculation. Chapter 4 discusses an alternative numerical simulation solver which

might outperform the conventional numerical simulation solvers.

As mentioned, conducting extensive experiment and numerical simulation for

obtaining accurate results for optimizing the performance of the flapping wing is

very time consuming and expensive. Therefore, a simple mathematical model can

be developed for reducing the time and cost for performing the optimization of

flapping wings by filtered the parameters which cannot generate significant lift.

3. Flow structure analysis

In this Chapter, lift enhancement mechanism (the leading edge vortex) has been

investigated by some researchers who conducted the flow visualization test on

living bat or insects. The thrust indicating vortex street (the reversed Kármán

vortex street) has also been found from swimming fishes. Hence, micro UAV or

UWV could employ and utilize these mechanisms for enhancing the lift and thrust.

In order to better understand the flapping wings aerodynamics, the flow structures

involved have to be studied in detail. Therefore, instead of repeating the study from

the above mentioned researchers for just comparing the flow structure across

different technique (experimental and numerical simulation) to prove the capability

of their solver, this thesis will conduct combined study based on force

measurement, numerical simulation and dye flow visualization to fully capture the

hidden fact behinds the flapping wings aerodynamic.

Hence, this thesis will investigate the corresponding areas, which are summarized

in the Table 2-2, in order to achieve the aims which are mentioned in previous

chapter.

Table 2-2 Scope of study

Flapping Motions Description Approach

Symmetrical

Heaving

Investigate the lift experienced by

the SD8020 which undergoing

symmetrical heaving

Experimental (force

measurement) and

numerical simulation

Symmetrical

pitching

Investigate the lift experienced by

the pitching flat plate in symmetrical

pitching manner

Experimental (force

measurement) and

numerical simulation

Symmetrical

pitching

Investigate the effect of flexibility to

the thrust by symmetrical pitching

SD 8020

Experimental (Dye

flow visualization and

force measurement)

Symmetrical

combined heaving

and pitching

Investigate the influences of the

phase different to the thrust from

combined pitching and heaving

SD8020

Experimental (Force

measurement)

Non-symmetrical

pitching

Evaluate the ability of pitching

SD7003 with non-symmetrical

pitching motion to lift generation

and investigate the effect of the lift

enhancement mechanism (Leading

Edge Vortex, LEV)

Experiment (Dye flow

visualization and force

measurement)

Chapter 3 Experimental Setup and Method

3-1 Overview

This chapter introduces the equipment used for current study. The equipment

which were utilized for the force measurement and dye flow visualization include:

water tunnel, force transducer, rotary DC motor, closed-loop servo stepper motor,

linear guide and dye pump (Figure 3-22). The selection of force transducer and

construction of experimental test rig is being discussed; error analysis for the force

measurement is also presented in this chapter.

3-2 Water tunnel

A water tunnel is an essential tool to generate free-stream water flow across a

submerged scaled model that enable users to investigate on the hydrodynamic

effects by conducting experiments such as force measurement, dye flow

visualization or Particle Image Velocimetry (PIV). As the water has a higher

density than air, the resistance force exerts on the moving object with same

geometrical property and travelling velocity is also higher. As a reason, the water

tunnel is primarily utilized in the study. Hence, with larger interaction forces

compared to air, the force measurement can be conducted with higher order of

force and allows obtaining higher accuracy results as the measuring range is closer

to the accuracy level of the force transducer. In addition, dye flow visualization and

PIV measurements are also easier to be implemented in water tunnel.

Figure 3-1 shows the water tunnel used for this study. This particular water tunnel

utilizes a centrifugal pump (with maximum pump rotational speed of 60Hz) that

generates a maximum free stream velocity of 0.2 m/s at the test section. The test

section is made from high transparency tempered glass and array of screeners is

used to ensure low turbulence intensity level at the test section. The contraction

ratio is 4:4:1 and details dimensions of the water tunnel are shown in Figure 3-2.

3.2.1 Water Tunnel Calibration

The calibration of the water tunnel was first conducted by using a pitot tube. The

calibrated free stream velocities (m/s) at the test section of the water tunnel, with

the corresponding water pump rotational speed (Hz), are shown in Figure 3-5.

Figure 3-1 Water tunnel

Figure 3-2 Dimensions of water tunnel

Figure 3-3 Drawing of DRUCK pressure sensor [39]

Electronic

Magnetic

Volumetric

Flow Rate

Meter

Water pump

(with electronic

rotational speed

controller)

(450 x 600) mm

cross sectional area

(4:4:1 contraction

ratio) and 1 m long

Test Section

Glass window

for camera

Parabola shape

End

Array of screeners

2 m

9 m

Drainag

e point

Figure 3-4 Cable connection diagram of the DRUCK pressure sensor [39]

Figure 3-5 Calibration result of water tunnel by pitot tube

Next, the turbulence intensity and uniformity of the water flow across the test

section of the water tunnel is measured by the Dantec Mini CTA (Constant

Temperature Anemometry) system [40]. The working principle of this CTA system

is illustrated in Figure 3-6. A CTA probe contains a very thin wire that is being

submerged into the stream. The amount of cooling on the wire by the flow provides

a measure for the flow velocity. As a thermal anemometry, the temperature across

the thin wire is being kept constant. As the free-stream passing across the wire, it

reduces the wire’s temperature and the system has to increase the current in order

to maintain the preset temperature. Thus, the change in the electrical current and

the heat exchanged can be cross-related in order to estimate the flow speed. The

advantage of the CTA system is that the flow velocity can be measured with a very

high temporal resolution which allowing the measurement of turbulent qualities.

Figure 3-6 Working Principle of Dantec mini-CTA system [40]

In this measurement, the Dantec mini-CTA uses a single wire probe made of thin

tungsten wire (1 mm long and 5 µm in diameter) for one dimensional flow

measurement as shown in Figure 3-7. The probe is then be heated up to 70 degree

Celsius by an electric current via a servo amplifier which is connected to one arm

of the Wheatstone bridge. The data acquisition was then performed by using a

National instrument (NI) Data acquisition (DAQ) card that is connected to the

workstation equipped with LabView with the sampling rate of 1000Hz.

Figure 3-7 Location of the CTA probe in the water tunnel test section

As shown in Figure 3-7, the CTA probe measurement plane is located at the testing

section of the water tunnel which measures 80% of the tunnel width which is the

location where all the force measurements will be made. In addition, measurements

were taken horizontally across the Y-axis and vertically across the Z-axis at 10 mm

intervals as shown in Figure 3-8 below.

Figure 3-8 Location of calibration plane (distance between measuring

points is for illustration only)

The flow speed measured by the CTA system is requires to be first calibrated with

a pitot-tube. Subsequently, the collected data will be converted and reduced into

the flow statistics using the following equations:

Mean velocity:

(3-1)

Standard deviation of

velocity:

(3-2)

Turbulence intensity:

(3-3)

(3-4)

This calibration shows that the water tunnel has an averaged Turbulence Intensity

(Ti) of 0.60% and a uniformity of 94.98%. The individual Ti and mean velocity,

Umean of each measuring location/point are plotted in Figure 3-9 and Figure 3-10.

Figure 3-9 Uniformity and Turbulence intensity across the test section

Figure 3-10 Uniformity and Turbulence intensity vertically from the surface

to bottom of the test section

3-3 Force Transducers

Since the dynamic measurement of small forces for flapping wings is very

demanding; it is important to select an appropriate force transducer. Thus, the

following three force transducers have been tested:

1. OMEGA LC-601

2. OMEGA LC-703

3. ATI (Gamma SI-32.2.5)

In order to confirm the accuracy of the data, these force transducers were

underwent the following tests:

1. Dead weight test

2. Dynamic test by oscillating cylinder (Chapter 5)

3-3-1 Force Transducer Suitability Analysis

First, the OMEGA LC-601 (1-axis) force transducer (Figure 3-11) was being

calibrated and tested. This force sensor has the lowest operating load (909g) and

provides the lowest full load scale error among these three force sensors. However,

the sensing area of this force sensor was vibrating during the measurement. Hence,

it was not selected as the vibration on the sensing area has seriously affects the

accuracy of the results.

Figure 3-11 Omega LC-601 force transducer [41]

The second force transducer is the OMEGA LC-703 (1-axis). The maximum

operating load of this force transducer is 5 Kilogram force (Kgf). Its dimensions

are as shown in Figure 3-12 (L = 38 mm, L1 = 14 mm, W = 14 mm, W1 = 9.5 mm

and H = 19 mm). Dead weight test on this particular force transducer was

conducted in order to validate its accuracy level. Dead weights of 10g to 100g with

10g intervals were measured by the force transducer. The results from the dead

weight calibration are plotted in Figure 3-13. 9000 data were collected per

measurement with sampling rate of 100Hz. The tabulated mean, maximum and

minimum values for each of data set from the respective measurements are shown

Sensing area

in Figure 3-13. Hence, the error which represents the difference between the mean

measured values to the actual weight of the dead weight can be obtained.

This force transducer needs a complex mechanism to direct and convert the applied

force to the measuring point as it can only measure the force in one direction

(single axis, tension and compression). This particular test rig will be further

elaborated in Section 3-4.

Figure 3-12 Omega LC-703 force transducer [41]

Figure 3-13 OMEGA LC-703 force transducer calibration results

Figure 3-14 Force orientation vector on the ATI Force Transducer [42]

For the third force transducer (ATI forces and torques sensors), the forces and

torques are recorded according to Figure 3-14. In order to reduce the hysteresis

effect and increase the strength and repeatability, the beams structure inside the

force transducer are machined from a solid piece of metal which allows the sensor

to be in a monolithic structure [42]. Besides that, the semiconductor strain gauges

are attached on three symmetrical beams inside the force transducer as sensing

element.

The ATI force transducer has a response time of 7x10-4

seconds and the resonance

frequency for axis Fx, Fy and Tz is 2KHz; Fz, Tx and Ty is of 1.4 KHz. With these

conditions, this force transducer is suitable for this study as the operating frequency

of the flapping foil is at the range of 101 Hz.

However, in order to ensure the collected data are accurate, dead weight calibration

was also conducted with ranging (X-axis) from 10g to 100g. 9000 data were

collected with the sampling rate of 100Hz. The calibration results in the mean,

maximum and minimum of the recorded weight are plotted in Figure 3-15. A

calibration report from the manufacturer is attached in Appendix III.

Figure 3-15 ATI force transducer calibration results (X-axis)

3-4 Construction of the Experimental Test Rig for Force

Measurement

This section discusses the selection of force transducer and the construction of its

corresponding experimental fixture for the force measurement. For the first design,

two sets of 1-axis force transducers (OMEGA LC-703) were used. A special

fixture was designed in order to allow the action force to be recorded by these 1-

axis force transducers (Figure 3-16).

Figure 3-16 Setups for double OMEGA LC-703 force transducer

From this particular setup, the action force ( ) can be obtained with the following

equation:

(0-5)

The major drawbacks of this setup is that the main frame is not strong enough to

hold the force transducers, especially in dynamic mode, due to the size of the test

model and the supporting bar that connected to the test model is rather large and

heavy. The whole apparatus became unstable when the oscillating frequency of the

motor was increased. Therefore, this set of apparatuses was abandoned.

The second design of the experiment fixture (Figure 3-17) uses only one set of

Force Transducer (OMEGA LC-703). The force transducer is mounted on a fixed

frame by a bracket (brown color); hence, the forces acting on the body will be

transferred by the ball bearing to the sensing axis of the force transducer. The

moving mechanism indicated in Figure 3-17 is responsible for generating the

rotation or linear motion for flapping hydrofoil.

Figure 3-17 Setups for single OMEGA LC-703 force transducer

Figure 3-18 Force diagrams

Figure 3-18 shows the force diagram for indicating the direction of forces in this

measurement. The actual force, FB, can be obtained by calculating the momentum

balance by the following equations:

(0-6)

(0-7)

FLC represents the force detected by the force transducer, ∆y1 is the distance from

the bearing to the force sensor, and ∆y2 is the distance from the bearing to the

centre point of the submerged portion of the model. However, this setup has too

many connections involved. Therefore, during high oscillating frequency test, the

fixture lost its stability. In addition, from Figure 3-17, friction exists between the

blue and yellow block affects the final force reading which is cannot be ignored.

(Further illustration on Figure 3-24)

Figure 3-19 Experimental setups for force measurement by ATI force

transducer

Due to the foregoing, the ATI force transducer was selected and replaced the 1-axis

OMEGA force transducer; the entire fixture was redesigned (Figure 3-19) as well.

The ATI force transducer was mounted to the fixed and stable frame in order to

represent the Global co-ordinate system (X-axis indicate thrust or drag, Y- axis

indicate lift or downward force). Thus, when the hydrofoil is moving, the forces

will be detected by the force transducer directly. With this setup, the experimental

structure is more sturdy and “cleaner” due to reduction of moving parts and simpler

design.

3-5 Actuation Equipment

Two sets of actuating mechanisms were utilized in this study for generating the

pitching, heaving (oscillating) or combined motions. The oscillating cylinder and

oscillating hydrofoil (SD8020) tests used a simple rotary motor that incorporated

with a linear guide for providing the linear oscillating motion (Figure 3-20).

The Cool Muscle high resolution closed loop stepper motor (CM-1, selected to

12,000 pulses per revolution) was used for the experiments on the symmetrical

pitching flat plate and SD8020 hydrofoil (Figure 3-21) as well as the non-

symmetrical pitching of SD 7003. An additional linear guide (THK linear guide)

and linear actuator (Coupled the THK actuator with additional Cool muscle high

resolution closed loop stepper motor) were used for the study of combined heave

and pitch motion. The overview of experimental equipment in this thesis is shown

in Figure 3-22.

Figure 3-20 Equipment and test rig for Oscillating test

Figure 3-21 Experiment setup for heaving and pitching of flat plate and

hydrofoil

Figure 3-22 Overview of experiment setup and equipment

3-6 Experimental Precautions and Data Processing

During dynamic measurement, natural frequency of the structure plays an

important role that influences the accuracy of data collected. Thus, it is vital to

avoid conducting the experiment on the natural frequency of the test rig because

operating a motor at the structural frequency will lead to serious vibration which

causes destruction of the structure.

Therefore, a free vibration test on the selected experimental test rig was conducted

in this study to obtain the structural frequency. An accelerometer was attached on

the experiment fixture during the measurement. The free vibration test was

conducted in two separate ways. First, the test was conducted on the main fixture

with an attached stationary hydrofoil that hanging in the air. Second, the test was

carried out on the main fixture with an attached hydrofoil that submerged in the

water.

Figure 3-23a indicates that the natural frequency of the main fixture obtained from

the first test (experiment setup with hanging hydrofoil in air) is 38.25 Hz. Next,

Figure 3-23b shows the natural frequency of the test rig with the hydrofoil

submerged in the water is 29.25 Hz. As the flapping frequency of this study does

not exceed 5 Hz, it can be concluded that the structure can be used for the force

measurements on the flapping hydrofoil.

Apart from the free vibration test, an experiment on flow over stationary foil was

conducted by numerical simulation and experimental approach for obtaining its

shedding frequency. The purpose of this test is to ensure the shedding frequency is

not within the range of the natural frequency of the test rig. The lift force collected

from this test was further converted from time domain to frequency domain by Fast

Fourier Transform (FFT) to determine the peak frequencies. Figure 3-23 (c) and (d)

show the lift in frequency domain by simulation and experimental approach. Both

methods produced the first peak frequency at 1.5Hz, which is representing the

shedding frequency. However, from the experimental approach (Figure 3-23b),

another peak frequency aroused at around 30 Hz. Refer to Figure 3-23 (a & b), the

natural frequency of the test rig is about 20-30Hz; Thus, this particular frequency is

the structural frequency of the test rig.

Figure 3-23 Natural frequency of the test rig without hydrofoil (a) and with

hydrofoil submerged in the water (b) & FFT from (c) simulation and (d)

experiment and structural frequency test (c) in air and (d) in water

a b

c d

Besides the above mentioned factors that might influence the accuracy of the

measurement, the inertia of the body motion has to be eliminated for obtaining the

results which is solely consists of the aerodynamic forces. Therefore, all tests were

conducted separately in the air and water.

Furthermore, by Nyquist-Shannon’s sampling theorem, the sampling rate has to be

doubled of the operating frequency. The operating frequencies involved in all the

experiments did not exceed 5 Hz. The selected sampling rate of the force

transducer used (ATI) is 20000 samples per second with an averaging level of 200,

resulting the final rate of sampling is 100 samples per second. Hence, this selected

sampling rate is suitable for our application in order to collect the entire range of

required signal.

In addition, the equipments were mounted on a fixed frame, which is isolated from

the water tunnel, in order to prevent the vibration from the pump of the water

tunnel to be detected by the force transducer. Furthermore, Butterworth filtering

was also applied with the cut off frequency which is doubled of the operating

frequency.

3-7 Experimental Error Analysis

The main sources of errors in this study can be identified from the force transducer,

water tunnel and the experimental fixture. Hence, this section discusses the error

analysis and identified the source of error for the force measurement tests. The

definition of errors includes firstly, the bias (or systematic) error, which can be

defined as the difference between the mean measured values to the true value and

secondly, the precision (or random) error is the measurement of randomness found

during repeated measurements [43].

Figure 3-13 reported the results from the dead weight test on the OMEGA LC-703

force transducer. The “error %” (bias error) represents the different from the

measured value to the actual value of the dead weight in percent. From this set of

dead weight test, the maximum bias error for this particular force transducer is

around 11%.

Besides the bias error of the OMEGA force transducer, another hidden source of

errors might be the friction between moving parts of the fixture and the stability of

the structure of the main fixture. Figure 3-24 indicates that two pieces (arrow

pointed) of the fixture are connected together by a screw. In this circumstance, the

screw might be over tightened and causing these two pieces of fixture unmovable.

Hence, a spacer with a diameter that is smaller than the bearing was used in order

to allow the fixtures to be rotatable so that the reaction force can be transferred and

recorded by the force transducer. However, for dynamic measurement, the

movement of the whole test rig will cause vibration and affect the measurement

especially at high oscillating frequency. Therefore, these factors can cause a serious

error in measurement and the uncertainty is hard to define.

Figure 3-24 Fixture for omega force transducer

Similarly, the dead weight test was also conducted for the ATI force transducer.

From Figure 3-15, the maximum bias error is found to be 4.5%. Besides that, the

dead weight test also shows that the ATI force transducer has a smaller bias error

and better measurement precision than the OMEGA force transducer. Furthermore,

this ATI force transducer allows the hydrofoil or the test model to be directly

attached without extra fixtures needed for the force measurement; hence, the above

mentioned factors of errors can be eliminated.

The uncertainties of the force transducer include the random and bias error [44],

therefore, the combined standard uncertainty uc for variable i can be defined as,

(0-8)

where us is the systematic error and si is the standard deviation. The combined

standard uncertainty for the OMEGA force transducer is more than 10%, and for

the ATI force transducer is around 5%. Although the OMEGA force transducer

Spacer is placed here

Bearing

claims to have a higher accuracy by the manufacturer, the total accuracy of the

force transducer combined with the required fixture results in an inferior accuracy

compared to the experimental fixture with the ATI force transducer. Therefore, the

final setup (Figure 3-19) with the ATI force transducer was selected.

The overall error is defined as the summation of all the possible errors from all

involved instruments. Hence, the estimated total error for the force measurements

that were being conducted in this thesis can be defined as:

Error Total = Error water tunnel + Error Force Transducer (0-9)

From the equation above, the error contributed by the water tunnel is 5%, and the

maximum error for the ATI force balance at the measuring range is also

approximately 5%. Hence, the total estimated error for the force measurement is

around 10%.

Chapter 4 Computational Method

4-1 Overview

This chapter presents a short review and discussions on various approaches used

for numerical simulation of flapping wings. The nature of flapping wing

aerodynamics is generally characterized at low Reynolds number regimes, which is

highly unsteady and transition from laminar to turbulent flow. As such, a solver is

needed to be able to model the turbulence effects accurately to predict the

performance of flapping wings. In particular, the interactions between the Leading

Edge Vortex (LEV) and the Trailing Edge Vortex (TEV) and their influence on the

lift and thrust generated need to be resolved.

Besides the unsteady turbulence effects have to be accurately modeled, the factors

for selecting an appropriate solver includes: manipulability, procedure for

preparation of mesh (pre-simulation stage), computational time and etc.

Conventional solvers with body fitted meshing approach are having difficulty on

meshing complex geometry and also hard for simulating moving object. In addition,

conventional solvers require co-ordinate transformation in order to solve the

governing equation and it is very time consuming. Hence, the following sections

highlight the background, advantages and some shortcomings of the selected solver

(Large Eddy Simulation with Immersed Boundary method).

4-2 Numerical simulation for Turbulence flow and Large Eddy Simulation

Amongst the various approaches to numerical simulation, the most accurate

approach for evaluating turbulent flows is the Direct Numerical Simulation (DNS).

This technique solves the instantaneous continuity and Navier Stokes equations

directly and is used in conjunction with an extremely fine mesh [45]. Shyy and Liu

[20] have performed series of simulations for flapping wings using DNS, which are

generally limited to very low Reynolds number (order of 102) on minuscule-scale

flyers such as insects. However, DNS is unsuitable for modeling animals which

travel in higher Reynolds number such as bird or bats as it requires large

computational costs [46].

Most commercial solvers are based on the Reynolds-Averaged Navier-Stokes

(RANS) approach [46]. Here, the Reynolds-decomposition of splitting the velocity

component into a mean value and a fluctuating value ( ) is

applied to the Navier-Stokes equation and then the time was averaged. In this

approach, the unclosed terms, which refer to the Reynolds-stresses, requires

additional closure. Turbulence models were developed in order to predict the

Reynolds stresses for the closure of the system of mean flow equations. RANS

turbulence models can be classified according to the number of additional transport

equations that needed to solve together with the RANS flow equation. For example,

the K-ε model requires the solution of two additional equations and the Reynolds-

stress model up to seven additional equations.

Since most RANS turbulence models are based on the eddy-viscosity approach,

which defines the eddy viscosity to account for the effects of turbulence; some

additional viscosity is introduced and thereby rendering accurate prediction of the

LEV as the LEV tends to be dissipated too quickly. In order to avoid the premature

dissipation of the LEV or TEV to numerical dissipation from large strokes of the

flapping wing that needed to be modeled, the RANS model is a less ideal solution

as it dissipates the LEV in addition to the numerical dissipation [25].

Taking into consideration with the above-mentioned factors, the Large Eddy

Simulation (LES) is an alternative approach for simulating the flapping wings. The

LES model solves the low-pass filtered Navier-Stokes equations instead of time

averaging [47] using a spatial filter to separate the larger and smaller eddies as the

small scale turbulences are more homogeneous and less affected by the boundary

condition than the large eddies and are also usually easier to model. In LES model,

the large eddies [47] or large vortex structures, which usually control the main

properties of a turbulent flow, are resolved (such as the LEV). Hence, the

unresolved scales in LES known as Sub-Grid Scale (SGS) turbulence are modeled.

Similar to Reynolds stresses in RANS, those unresolved small scale eddies is

describe as the SGS stresses and require an SGS model in order to close the system

equations.

As for the filtering process for LES, spatial filtering technique is employed on the

unsteady Navier Stokes equations in three dimensional spaces and removes the

scales of wave-numbers higher than the cut off wavenumber. The filter function

G(x, x’, ∆) is applied to the velocity field, the filtered velocity flow field is

therefore can be represented as follow [37]:

(4-1)

Where U is the unfiltered flow field and ∆ is the filter cutoff width. The

cutoff width (∆) is normally defined as the cube root of the grid or cell volume:

(4-2)

Hence, after the application of filtering on the Navier Stokes equation, the filtered

Navier Stokes can be represented as follow:

(4-3)

The SGS unresolved scales are represented in the last term on the right side of the

filtered Navier Stokes equation and the SGS tensor can be defined as:

(4-4)

The filtered continuity equation for incompressible flow can be described as:

(4-5)

From Equation (4-7), as mentioned, the SGS stresses have to be modeled by the

SGS model in order to close the system. The standard Smagorinsky model [46] was

developed by Smagorinsky in 1963. In this model, the SGS stress tensor is defined

as the filtered rate of strain tensor and the turbulent stress tensor can be

represented in diffusive form as follow,

(4-6)

is the eddy viscosity at the subgrid scale, . is the Smagorinsky

constant , is the filtered width and

; the filtered strain rate

tensor are,

(4-7)

However, there are several drawbacks for this standard model as it changes the

model parameter CS from one case to another. The energy is also unable to transfer

from unresolved smaller scales back to the larger scales. Bardina [46] has proposed

an advanced SGS model by applying two filtering operations. In dynamic model,

the parameter is calculated dynamically as it is re-adjusted according to the local

flow conditions by applying a second test filter that is larger than the grid filter.

The resolved turbulent stresses is,

(4-8)

The subtest stress (STS), is equal to ; the SGS stress and the STS

are therefore can be modeled and represented in diffusive form as,

(4-9)

(4-10)

From above equations, the resolved stress has become,

(4-11)

However, the above mentioned dynamic model cannot calculate the model

parameters directly and requires further modeling. Thus, in 1986, Germano [46]

proposed a different approach to decompose turbulent stresses which formed the

basis of the dynamic SGS model. The SGS and STS stresses in Germano proposed

model are,

(4-12)

(4-13)

The dynamic constant is,

(4-14)

Germano suggested that the model parameter has to be in homogeneous direction

for avoiding numerical instabilities when the denominator of the dynamic constant

( ) becomes zero. This particular dynamic model was reviewed by Leisieur and

Metais (1996) than by Maneveau and Katz (2000) [46]. The advantage of this

dynamic model is that the constant of the Smagorinsky model is computed from

the resolved flow field, and hence, does not need to be defined beforehand.

The LES computation can be done with less effort and less computational time

than a comparable DNS computation although it still requires fine meshes [45]. As

such the computational costs are still higher than a RANS simulation. However,

since the Large Eddy Simulation (LES) is an inherently unsteady approach, it is

more suitable for the solution of transient cases combining the advantages of the

DNS and RANS methods [47]. The LES approach with Germano proposed

dynamic SGS model was therefore chosen for the numerical simulations in this

thesis.

4-3 The Immersed Boundary (IB) method

Most of the conventional CFD codes use body fitted meshing technique for the

discretization of the flow domain. However, for moving bodies within the flow, it

requires re-meshing of the flow domain at every time-step. This can be time-

consuming as well as a source of error as the automatic meshing between time-

steps can yield distorted cells and negative volumes. This study uses a different

approach, the Immersed Boundary (IB) Method, to describe the moving body

inside the flow and the governing equations are formulated on a simple Cartesian

grid. The body is represented with a body force term in the governing equations.

As such, the body is “immersed” in the grid as shown in Figure 4-1, and is not

aligned with the mesh cells. The “immersed” body in the domain can be defined as

a series of linked points.

Figure 4-1 An immersed body in the simple Cartesian grid; Ωb as body

with boundary label as Гb and fluid domain Ωf

The IB method has been formulated first by Peskin [48] for the purpose of

simulating the blood flow in the heart. The main advantage of the IB method [49]

is the simulation of moving objects in the flow. This is because the grid does not

need to be re-generated for each time step – which is the key difference from body

fitted mesh methods [50].

The movement of the object boundary is incorporated simply by changing the body

force term rather than re-meshing the flow domain and is hence, computationally

less expensive [51]. In addition, complex geometries that are difficult to mesh

using body-fitted meshes can also be solved with the immersed boundary method

as only one Cartesian mesh is required. Furthermore, the simulation of the flow

phase is very efficient as the solver can be optimized for an orthogonal hexahedral

mesh. Since the code is based on the Navier Stokes equation (Equation 4-15); we

can assume:

L =0; in Ωf (fluid domain) (4-15)

Where Г on Гb; L(U) indicates the governing equation in the fluid with the

domain of Ωf; L is the operator of the Navier-Stokes equations and . Гb

represents the boundary of the immersed solid body Ωb (Figure 4-1). In the

conventional CFD code, the governing equation will be discretized into the body

fitted grid, which is followed by the boundary conditions applied at the boundary

grid point Гb. However, in the immersed boundary (IB) method, the forcing

function will instead be added to the governing equation and can be classified into

two approaches - the continuing forcing approach and the discrete forcing approach.

For the solver that is employed in this study, a discrete approach was implemented.

From Equation (4-16); the first two terms on left hand side represent the inertia

term; while the right hand side represents the divergence of stress and body forces

term.

(4-16)

After the Navier Stokes equation have been discretized; on a particular grid point

(I,j,k) with the array of [nx, ny, nz] in x, y, z direction, the discretized equations

can be represented as:

(4-17)

(4-18)

(4-19)

The right hand side vector

includes convective, diffusive and pressure

term that were being calculated at the intermediate time step of . At the

moment when the particular point coincides with the immersed boundary, the

discrete boundary condition is applied and the forcing term becomes:

(4-20)

The boundary force is applied on the grid next to the immersed boundary and

interpolated on the contour. The flow inside the immersed boundary is set to zero

and no forcing term will be included on these grids. The boundary force is

calculated at PB, which is next to the point P1 (equivalent to immersed boundary

point PIB) by interpolating the condition given from the surrounding grid points

from P1 to P4 (Figure 4-2).

Figure 4-2 Boundary force conditions [52]

The pressure condition applied in the immersed boundary method is the same as

the methods from body fitted or staggered grid. The pressure boundary condition

for non-moving immersed boundary and the von Neumann pressure boundary

condition are applied on the boundary of the body.

(4-21)

Figure 4-3 Location of immersed boundary

However, the location of the immersed boundary is important for the

implementation of the pressure boundary condition. In Figure 4-3, the left graph

indicates that the last interior point is a cell center of the grey color cell, while the

right graph indicates that the last interior point is the staggered grid point.

Therefore,

(4-22)

For the first case, the pressure condition can directly utilize the traditional approach

for body fitted staggered grids by setting pi-1 = pi. However, for the second case,

the face W is an interior point and the pressure gradient is not equal to zero.

Therefore, in order to apply the pressure boundary condition, it needs the

information from the boundary point B, subsequently interpolating from point B to

the grid point on the cell face W.

The method of applying the boundary condition on a body-fitted or staggered-grid

is to set the pressure value of first exterior point PB equal to first interior point Pp

(Figure 4-3, left). Hence, this particular approach inspired the method of setting the

pressure boundary condition on the immersed boundary method.

Figure 4-4 Location of Pp and PB [42]

(4-23)

a) b)

(4-24)

(4-25)

From Figure 4-4b, the pressure at PB can be calculated by its neighbor values and

with the direction normal to the immersed boundary. The pressure ( on a

particular grid can be represented by Equation (4-23).

Figure 4-5 Simulation setup (masking)

For the dynamic mode of simulation, the IB method requires the mask to be re-

generated for every time step (Figure 4-5). However, the same mesh will still be

used. The co-ordinate of the object will integrate with the code that allows it to

move (translating, rotating or combined translation and rotation) relative to the

original position. The velocity boundary condition (on the boundary) for moving

non-slip wall can be represented as:

Г Г (4-26)

Lastly, the pressure on the moving boundary can be represented as:

(4-27)

Figure 0-6 Pressure boundary conditions

As discussed in the beginning of this chapter, body fitted approach requires highly

skilled person to perform the meshing for complex geometry. Besides that, the

preparation for conducting simulation of moving object is also tedious. Therefore,

IB method seems promising for improving the shortcomings from the conventional

solver as IB method only uses a simple Cartesian mesh which does not require re-

meshing at every iteration for simulating moving object; in addition, no

transformation of co-ordinate is needed for solving the governing equation; hence,

the pre-simulation stage can be easily performed. In addition, Gianluca [53] also

stated that the calculation from IB method is more efficient than the conventional

CFD approaches.

However, there are some shortcomings for the IB method; for example, similar to

RANS solver; IB method is also having difficulty on handling geometry with sharp

edges [37]. Apart from that, most of the IB techniques are having difficulty on the

issue of mass-conserving at the moving boundary, and causes wiggles appear

around the moving object and high frequency oscillation noise appeared on the

forces and pressure curve. Therefore, ghost cells and cut cell method were

developed for solving this difficulty although these approaches will complicate the

solver code. Hence, besides these two methods, the effect from wiggles or high

frequency peaks can be resolved by reducing the time steps from a particular grid

resolution or improving the grid resolution from a fixed time step (Figure 4-7) [54].

Figure 4-7 Time history of pressure drag coefficient for oscillating cylinder

on different grid resolution with fixed time step of 0.002 seconds (left) and

different time step with fixed grid resolution, D/dx = 16 (right). [54]

As a conclusion, due to all the shortcomings from the conventional solver with

body fitted meshing approach which employed RANS turbulence model, the Large

Eddy Simulation (LES) with Immersed Boundary (IB) method was evaluated for

its ability on flapping wings study in this thesis. The development of the LES flow

solver, which is selected for this thesis, will be discussed in the next section.

4-4 The Flow Solver

The original LES solver was developed and validated by Pierce [47] for the

simulation of variable density flows with non-premixed combustion. The

incompressible part of this solver was used for this study and combustion and

scalar transport were not considered. The code is based on the finite volume

method using staggered grids and on three dimensional Cartesian grids. The

geometrical properties in the z-direction were kept constant for efficiency as well

as the principal motion in this study is remained in two dimensional (Heaving and

pitching in X-Y plane).

In order to solve the momentum equations, current solver uses a pressure

correction technique. An initial “guess” pressure value will be used to calculate the

velocity flow field where the momentum equations are solved by iterative, semi-

implicit technique and only the cross flow direction is treated implicitly. Next, in

the correction step, Fast-Fourier transform is only applied to the z-direction of

pressure Poisson equation and compute the “corrected” pressure, followed by

updating the velocity. This “correction” procedure will be repeated until the

velocity field is converged.

Besides that, first order Runge-Kutta method is employed for the first iteration and

the Poisson equation is solved in order to determine the pressure field by Multi-

Grid (MG) or Successive Over Relaxation (SOR) solver. The Immersed Boundary

(IB) method is implemented in the code for simulating the moving boundary. The

original code was verified by Heieck [31], Theissen [49] and Zhang [55].

4 -5 Simulation Setup and Summary

In this thesis, numerical simulations on the oscillating cylinder, heaving hydrofoil

(SD8020) and pitching of the flat plate were conducted for evaluating the accuracy

of current solver. The example of the mesh structure (resolution: 320 x 320 x 32) is

shown in Figure 4-8, with a two dimensional hydrofoil located in the denser region.

The length and width of the control volume for this simulation is labeled in terms

of the chord length (c).

Figure 4-8 Grid resolution of 320x320x32

In order to validate the results from the numerical simulation with the experimental

approach, the boundary and flow conditions have to be fixed across these two

approaches. Therefore, the free-stream velocity (Reynolds number), size of model,

dimensions of control-volume and the moving frequency of the model are in the

same scale. Apart from the above conditions, the neighboring meshes from the

immersed body, including the entire area of moving boundary, are finer as

compared to the meshes from another location. The purpose is to reduce the

computational time for doing fewer calculations in less important areas.

The Courant Friedriches Lewy (CFL) numbers, which were investigated in this

study, are ranged from 0.1 to 1. Within a simulation, the CFL number was fixed

instead of fixing a constant time step for maximizing computing speed. The CFL

number is also known as the Courant number. It is defined as the ratio of the free-

stream velocity to the fraction of the dimensionless length of transport per time

step from the simulation. In addition, the input parameters have to be converted

into a dimensionless value as below:

i) Reynolds number, Re,

(4-28)

ii) Dimensionless oscillating amplitude, ,

(4-29)

iii) Dimensionless Oscillating frequency (Strouhal Number), St,

(4-30)

where ρ is the density of the fluid, μ is the dynamic viscosity of the fluid, V is the

free-stream velocity, A0 is the actual oscillating amplitude, d is the reference length

and f0 is the actual oscillating frequency.

Throughout a simulation run, the reference length has to be fixed. For example, the

reference length (d) for the oscillating cylinder is the actual diameter of the

cylinder; the reference length in this case has to be fixed across Equation (4-28) to

(4-30). For the pitching and heaving hydrofoil and flat plate, the reference length is

referring to its corresponding chord-length c.

In this chapter, the discussion on various turbulence models, the pros and cons of

body fitted and immersed boundary approaches, and also the development of the

current solver is presented. In summary, due to the unsteadiness of flow generated

by flapping wings and the shortcomings of the conventional simulation solver, this

thesis evaluated a novel numerical solver, which employed the LES turbulence

model with the IB method, for the study of flapping wings.

4-5 Grid Independence Test

In numerical simulation, the mesh resolution is a very important factor affecting

the accuracy of the calculations. The results may be inaccurate if the mesh is too

coarse and the computational time will be significantly large if the mesh resolution

is too high. Hence, this section presents one of the grid independence tests from

this study. In order to obtain suitable mesh resolution for accurate numerical results,

three different mesh size, 64 × 64 × 32; 192 × 192 × 32 and 384 × 384 × 32 were

applied for conducting the grid independence test.

This grid-independence evaluation is based on the test case of a symmetrically

pitching flat plate with pitching amplitude of 20 degrees and rotational speed of 50

degrees per second; the corresponding Rechord is 8000. These parameters are

exemplary for all simulations conducted here. Figure 4-9 shows the simulation

results with various mesh resolutions. The lift coefficient obtained from the mesh

resolution of 384 × 384 × 32 and 192 × 192 × 32 are almost identical. Therefore,

the mesh resolution of 192 × 192 × 32 is considered adequate for this study.

Lastly, the parameters and simulation-conditions utilized for all prior work,

together with an overview of the numerical simulation are summarized in Table 4-1.

Figure 4-9 Lift coefficients versus time plot

Table 4-1 Overview of the numerical simulation

Oscillating

cylinder Heaving SD8020

Pitching Flat

plate

SGS model Dynamic Smagorinsky model

CFL numbers 0.1 – 1

Reynolds

number 4,000 192,000 4,000 to 192,000

Number of time

steps for initial

divergence limit

20

Number of

iterations per 10

time step

Convergence

tolerance 10

-3

Mesh resolution

192 x 192 x 32

384 x 384 x 32

192 x 192 x 32

320 x 320 x 32

480 x 480 x 32

64 x 64 x 32

192 x 192 x 32

384 x 384 x 32

640 x 640 x 32

Chapter 5 Results and Discussion

5-1 Chapter Overview

This chapter presents and discusses the results obtained from the experiments and

numerical simulations. The main factors which affect the flapping wings’

generation of lift and thrust are as follows:

Flapping frequency,

Flapping amplitude,

Flapping pattern (the heave, pitch or both),

Reynolds number (factors of density, free-stream velocity, geometrical

property and dynamic viscosity of the fluid).

A series of experiments (including direct force measurements, dye flow

visualizations) and numerical simulations were conducted to study flapping wings’

aerodynamics, these tests include:

1. Investigation to validate the result obtained from CFD solver to

experimental setup for dynamic force measurements on an oscillating

cylinder in a free-stream.

2. An oscillating hydrofoil was studied to further validate the CFD solver data

so as to determine the capability of the symmetrical heaving mode to

generate lift and thrust.

3. A symmetrical pitching flat plate was studied through both CFD and

experimental approach at different free-stream velocities and pitching

parameters to ascertain its lift performance. Apart from that, a simple

mathematical model for predicting lift from pitching flat plate was

developed based on this set of study (Chapter 6).

4. Dye flow visualization and direct force measurement was conducted on

symmetrical pitching SD8020 (with and without flexible trailing edge

extension) to evaluate the effects of flexibility of flapper to the thrust.

5. The lift enhancement ability of the Leading Edge Vortex (LEV) was

investigated through direct force measurement and dye flow visualization

on non-symmetrical pitching of SD 7003 hydrofoil.

5-2 Oscillating Cylinder

The ability of the current experimental test rig and the CFD solver to obtain

accurate measurements of small scale dynamic forces is important. Hence, static

dead weight test on the force transducer and calibration of other equipment were

conducted. Additionally, an oscillating cylinder test were performed to ensure the

credibility of the research data as the results obtained from this oscillating cylinder

test were validated to the results from the literature of Gopal [56]. Referring to

Gopal’s study, the force measurement was conducted in two phases: firstly, in

water and secondly, without water (in air) to eliminate the inertia effects from the

oscillating cylinder.

The non-dimensional frequency (Strouhal number) is defined in the following

equation,

(5-1)

where f0 is the actual oscillating frequency, d is the reference length (diameter of

cylinder) and u is the free-stream velocity. The oscillating motion is described in

the following equation,

(5-2)

where Y is the maximum amplitude.

The experimental setup for oscillating cylinder is shown in Figure 5-1. The

cylinder is attached to the force transducer; a linear guide is used to convert the

rotary motion into a linear oscillating motion. The cylinder oscillates in sinusoidal

motion with fixed amplitude in the cross-wise direction (Y-axis). The fluid flows

past the cylinder in the perpendicular direction (X-axis). The same non-

dimensional parameters applied in the Gopal’s study were re-used for ease of

comparison.

The diameter of the cylinder is 25 mm and the ratio of oscillating amplitude to

cylinder diameter is 0.3. The test was conducted at Recylinder of 4,000 which

corresponding to the free-stream velocity of 0.16 m/s. A force transducer is fixed

between the cylinder and the linear guide, with a sampling rate of 100 samples per

second. Following the Nyquist-Shannon sampling theorem, this sampling rate is

adequate, given that the maximum operating frequency is only 1.5Hz. Butterworth

filtering was also applied at the cut off frequency of 5 Hz to filter any unwanted

noises.

Figure 5-1 Experimental Setup

Figure 5-2 Simulation setup

The numerical simulation setup for the oscillating cylinder is shown in Figure 5-2.

The parameters involved were cross-referred to the Gopal’s test. The cylinder is

located in between two free slip walls. The direction of flow is from the left toward

the right with the prescribed Reynolds number. Similar study has also been

conducted by Zhang [57] and Theissen [49], therefore, the grid independence test

was not conducted in this work.

The following three parameters are measured from the study: First, mean drag

coefficient (Cdm), which is defined as averaged value of instantaneous drag

coefficient over a time period T (Equation 5-3). The second and third parameters

(Equation 5-4 and 5-5), which include oscillating drag (Cdo) and oscillating lift

(Clo), was defined as the standard deviation of the mean drag or lifts coefficients

(Cdm or Clm) respectively.

(5-3)

(5-4)

(5-5)

Cdo denotes the oscillating drag coefficient. Clo denotes the oscillating lift

coefficient and N is the total number of experiment data. The drag coefficient (Cd)

and lift coefficient (Cl) obtained for the oscillating cylinder test are presented in

Figure 5-3 and Figure 5-4.

Figure 5-3 Oscillating Lift Coefficient versus non-dimensional frequency

Figure 5-4 Mean and oscillating drag coefficient versus non-dimensional

frequency

From Figure 5-3 and Figure 5-4, the magnitude and the trend of the lift and drag

coefficients determined by the CFD solver and force measurement are considerably

close to the literature data. The sudden increased in these coefficients between the

Strouhal number of 0.15 to 0.2, which is due to the resonance of the oscillating

frequency and the natural shedding frequency [56], can also be predicted by current

solver and test rig. The main reason for the experimental oscillating drag

coefficient to be relatively larger is due to the minuet range of force measured,

which is below the order of 10-2

N. At high Strouhal number, the actuating

mechanism that converts the rotary motion to linear motion became unstable, thus,

the excessive vibration on the test rig caused the drag reading to fluctuate.

Therefore, in order to avoid excessive structural vibration, another set of test rig is

developed and employed for the rest of the study.

Although the measured forces are extremely small (in the scale of 10-2

N and

below), the results reflected from the current experimental setup and computational

method agree considerably with the literature results in determining the dynamic

forces (10-2

N and above, from mean drag coefficient). In conclusion, since the

scale of measured forces for flapping wings study is above the scale of 10-1

N and

coupled with the dead weight test, the accuracy of the results obtained for the

flapping wings study can be assured. Furthermore, with this particular test, the

limit of the test rig, the force balance and simulation solver can be determined.

5-3 Symmetrically Heaving/Oscillating SD8020 airfoil

Having established the accuracy of the experimental setup and the LES solver in

predicting forces of periodically oscillating bodies at low Reynolds numbers, the

setup and solver were applied to an oscillating hydrofoil (SD8020), to assess its

ability to create lift and thrust.

In this section, the experimental setup (Figure 5-1) was identical to the oscillating

cylinder experiment described in the previous section. The airfoil has a chord-

length of 120 mm and a span-width of 400 mm. The corresponding flow condition

is Rechord of 19200 (free-stream velocity of 0.16 m/s); the heaving amplitude of the

oscillating foil is 5 mm and four different heaving frequencies are applied. The

properties of the flapper are highlighted as below:

Flapper profile : SD 8020 (experimental)

SD 8020 with truncated trailing edge (Numerical simulation)

Chord-length :120 mm

Span-width : 400 mm

Pivot point : Quarter chord

Non-dimensional parameters corresponding to the experiment parameters were

used for the computational analysis. The sharp trailing edge of the airfoil (Figure

5-5, right) was modified slightly to avoid its appearance within a single cell which

causes difficulties in numerical modelling given that no unique boundary condition

exists. The simulations were run on 8 processors over 5 periods. It took 3 days to

complete a simulation with mesh resolution of 320 x 320 x 32 and one week to

complete the simulation with mesh resolution of 480 x 480 x 32.

Figure 5-5 Simulation setup (left) and Truncated trailing edge SD8020 for

numerical simulation (right) [58]

Figure 5-6 Motor rotational frequency for heaving motion of SD8020

Figure 5-7 Lift coefficient (Cl) versus time plot (Simulation and Experiment)

from heaving airfoil with heaving frequencies of (a) f = 0.833Hz, (b) f =

1.083Hz, (c) f = 1.283Hz and (d) f = 1.5Hz

Figure 5-7 compares the lift coefficients from the heaving hydrofoil by experiment

and numerical simulation. The experimental results are represented by blue dots

while the simulation results are represented by the continuous red curve. The range

of the oscillating frequency is from 0.833 Hz to 1.5 Hz which corresponds to the

Strouhal numbers of 0.5 to 1.

The trend and magnitude of these results obtained from both approaches are having

good agreement. At lower frequencies, the disagreement is due to the deterioration

in the accuracy of the force transducer in the measurement of small forces. The

error bars in Figure 5-7 show the manufacturer’s estimate of the maximum error

(0.24 N). At low frequencies, the loads are small and lead to a large relative error in

a) b)

c) d)

the readings. At higher frequencies, the relative error decreases and the agreement

between experiment and simulation results improve. Cross checking the

experimental data, the computational data allows an assessment of both approaches

since possible sources of errors in one approach may not be present in the other.

Next, it is also possible for this set of experiments to examine the symmetrical

oscillating airfoil’s ability to generate lift. It can be seen from Figure 5-7 that the

magnitude of the peak of the lift curve increases with higher oscillating frequency.

This is because the increase in oscillating frequency causes greater momentum of

the fluid transferred to the hydrofoil. As the heaving direction is changed suddenly

when the airfoil reaches the maximum heaving amplitude, the peak of the

aerodynamic forces is produced [34].

However, the positive lift from the first half heaving cycle is always cancels out

with the negative lift from second half heaving cycle. As a result, the averaged lift

over entire heaving cycle is always zero. On the other hand, the results show that a

half-cycle of the flapping motion with higher flapping frequency might be able to

produce significant lift. Hence, in order to produce a non-zero averaged lift, the

second half-cycle of the flapping motion needs to be altered or adjusting the

flapping frequency to reduce the downwards force. In order to discover a suitable

flapping pattern which is able to produce lift, other types of flapping motions

(symmetrical and non symmetrical pitching motion) will be investigated.

5-4 Symmetrical Pitching of Flat Plate

In this section, the study on symmetrical pitching flat plate with different

combinations of pitching amplitudes and rotational speeds is discussed, since the

tests from the previous section were unable to obtain a set of flapping parameters

which can produce significant positive averaged lift as the pitch-only motion is the

other extreme compared to the heave-only motion. Hence, this section provides

results on the pitch-only motion spectrum. Experiments on non-symmetrical

pitching modes will be presented in Section 5-6.

Figure 5-8 Experimental setup (left) and Numerical setup (right)

Force measurement and numerical simulation were also conducted on a flat plate

with symmetrical pitch-only motion in this set of study. The DC rotary motor was

replaced by a high resolution Cool-Muscle stepper servo motor. The flapper

properties are as below:

Flapper Profile : Flat plate Span-width : 320 mm

Chord-length : 120 mm Pivot point : Quarter chord

X

Y

The differences between the symmetrical and non-symmetrical pitching mode are

illustrated in Figure 5-9. For symmetrical pitching motion (Figure 5-9a), the up-

pitch and down pitch angles and speeds are equal (α1 = α2 and ω1 = ω2). However,

in non-symmetrical pitching motion (Figure 5-9b), the up-pitch and down pitch

angles and speeds are different (α1 ≠ α2).

Figure 5-9 (a) Symmetrical and (b) Non symmetrical pitching up and down

motion

5-4-1 Investigation into the effects of the pitching parameters and free-

stream velocity on lift in the symmetrical pitching mode

This sub-section compares the results obtained from the numerical simulations

(LES) and force measurements on an oscillating flat plate which was undergoing

pitch-only motion. Investigations on this particular pitching mode on the lift can be

divided into two areas: First, the effect of pitching parameters with fixed free-

stream velocity, and second, the effect of free-stream velocity with fixed pitching

parameters. Table 5-1 summarises all the pitching parameters and their

corresponding Reynolds numbers in the conducted tests.

a) b)

Table 5-1 Pitching parameters and its corresponding Reynolds numbers

Pitching parameters Reynolds numbers

Pitching amplitude (α): 40 degrees

Rotational Speed (ω) :

100degree/second

4000 & 19200


Rotational Speed (ω) : 50

degree/second

4000 & 19200


Rotational Speed (ω) : 100

degree/second

4000, 8200, 12240, 16320 & 19200

The phase-averaged time history lift coefficients plots from the LES computations

and force measurements for these tests mentioned in Table 5-1 are shown in Figure

5-10 and Figure 5-11. The error bars shown in these graphs are labelled according

to the maximum error given by the manufacturer’s specification (0.24 N). Phase

averaging was applied to the results obtained from the LES computations (3

pitching cycles) and the force measurements (10 pitching cycles). Similar to the

previous set of studies, Figure 5-10 and Figure 5-11 show that the results from

simulation and experimental approach are close to each other in term of trend and

magnitude. However, the discrepancy between these results might due to the sharp

corner of the pitching plate existed in the simulation. Apart from that, the motion

provided by the actuator might be slightly different to the prescribed motion in

numerical simulation. In order to obtain better agreement between these approaches,

the time-step or the grid resolution plays as a very important role.

Re = 4000 Re = 19200

Figure 5-10 Time history of phase averaged lift coefficient plots of pitching

flat plate at Reynolds number of 4000 (left column) and 19200 (right column)

Re = 8200

Re = 12240

Re = 16320

Figure 5-11 Time history of phase averaged lift coefficient of pitching flat

plate with pitching amplitude of 20 degrees and pitching speed of 100

degree/second at Reynolds number of 8200, 12240 and 16320

The following section discusses the effects of pitching parameters and Reynolds

number to the lift. These results were re-arranged from Figure 5-10 and Figure

5-11 for the ease of comparison. The rationales for presenting the following charts

in lift force instead of lift coefficient are, firstly, to reflect the actual measurement

scale. Secondly, to compare the results across different Reynolds numbers. The lift

coefficient for the cases with smaller force and very low free-stream velocity might

be higher than the cases which have a larger lift but experiencing higher free-

stream. Hence, in this circumstance, investigation of lift performance by lift

coefficient is inappropriate.

To examine the effect of pitching amplitude, the following tests were conducted.

The Reynolds numbers was fixed at 4000, corresponding to a free-stream velocity

of 0.034 m/s. Figure 5-12 shows that, at the pitching speed (ω) of 100

degree/second, the pitching amplitude (α) of 40 degrees has a higher peak value of

lift and it is almost 2.5 times higher than pitching amplitude of 20 degrees.

Figure 5-12 Phase averaged lift force of pitching flat plate with α=20 degrees

and 40 degrees to fixed ω = 100 deg/s at Re = 4000

Next, in order to investigate the effect of pitching speed, the Reynolds number was

fixed at 4000 and the pitching amplitude was also fixed at 20 degrees. The selected

pitching speeds were 50 degrees per second and 100 degrees per second. Figure

5-13 shows that higher pitching speed allows higher lift peak to be produced. The

peak lift from the red curve for rotational speed of 100 degrees per second is 3.75

times higher than the blue curve (50 degrees per second).

Figure 5-13 Phase averaged lift force of a pitching flat plate with pitching

amplitude of 20 degrees and pitching speed of 50 degree/second and 100

degree/second

For the following study, investigations on the effect of the free-stream to the

pitching plate were conducted across two test cases. First, the pitching amplitude (α)

was 20 degrees and the pitching speed (ω) was 50 degrees per second; and the

second case, the pitching amplitude was 40 degrees and the pitching speed was 100

degrees per second. The Investigated Reynolds number were 4000 and 19200.

From Figure 5-14, which corresponds to the case of fixed pitching amplitude of 20

degrees and pitching speed of 50 degree per second, it shows that with the

increases in Reynolds number, the peak value of lift is also increased from 0.4 N to

almost 2.5 N.

In another situation, for larger pitching amplitudes of 40 degrees (beyond static

stall angle of attack) with fixed pitching speed; Figure 5-15 shows that, the same

magnitude of lift peak is produced across the Reynolds number of 4000 and 19200.

Therefore, it shows that, increases of the Reynolds number does not increase the

magnitude of the peak of lift for the pitching amplitude which is beyond the static

stall angle.

Figure 5-14 Lift curve for pitching flat plate with pitching amplitude of 20

degrees and pitching speed of 50 degree/second to the Reynolds numbers of

4000 and 19200

Figure 5-15 Lift curve for pitching amplitude of 40 degrees and pitching

speed of 100 degree/second with Reynolds number of 4000 and 19200

Figure 5-14 shows that increases of Reynolds numbers leads to increases of the lift

peak magnitude with fixed pitching parameters. Figure 5-14 and Figure 5-16 also

show that the Reynolds number is the dominating factor for influencing the peak

magnitude of lift but with the pitching amplitude lower to the static stall angle of

attack.

Therefore, the above presented results (Figure 5-12 and Figure 5-13) indicate that,

larger pitching amplitude and speed are suitable for the flapping vehicles to

generate high lift or thrust at the beginning of flight in order to take off or

accelerate from slow speed. The results from Figure 5-15 shows that large pitching

amplitude is unable to increase the lift peak at high Reynolds number; but Figure

5-14 further reveals that lower pitching amplitude will be more suitable for

retaining lift or thrust during high travelling speed as the lift increased significantly

with higher Reynolds number.

Since large pitching angle, which is above static stall angle of attack, did not able

to obtain higher lift while increasing the Reynolds number, therefore, in order to

have detail investigation of the effect of free-stream, both force measurement and

numerical simulation were performed with the following conditions:

Reynolds numbers: 4000, 8200, 12240, 16320 and 19200;

Fixed pitching parameters of:

Pitching amplitude, α = 20 degrees

Pitching speed, ω = 100 degree/second

Figure 5-16 Lift curve for pitching amplitude of 20 degrees and pitching

speed of 100 degree/second from Re of 4000 to 19200

Figure 5-16 shows that, the peak lift increases with the higher Reynolds number

although the pitching parameters were fixed. This results further showing that, for

lower pitching amplitude (lower or around static AOA), increasing the free-stream

velocity could increase the lift. Hence, this set of parameters could be tuned for the

vehicle to obtain high lift while cruising in higher speed.

However, for all of the mentioned cases above in symmetrical pitching mode, the

averaged lift over the entire pitching cycle is still approximate to zero as the

positive lift from the first half cycle is always cancelled off by the second half

cycle. Next section presents the image sequences obtained by the LES with IB

computation in vorticity plots and further discuss the causes of the inability of

positive lift generation by symmetrical pitching mode from these particular

combinations of pitching parameters.

5-4-2 Image sequence for vorticity plot of pitching flat plate

In this section, the images sequence in term of vorticity, from the pitching flat plate

obtained by the Large Eddy Simulation (Mesh resolution of 192 x 192 x 32) are

presented. The images were extracted from EnSight 90 and the pitching parameters

for pitching plate at different free-stream velocities (Rechord of 8200, 12240 and

16320) are fixed and tabulated as below:

Flapper profile : Flat plate Rotational speed : 100 deg/s

Pitching amplitude : 20 degrees Pivot point : Quarter chord

The images are represented in the Z-component vorticity, which can be calculated

from Equation (5-6). The blue and red colour in the image sequences indicates

vortices in the clock-wise and anti-clock-wise rotations respectively.

(5-6)

where . The overview of pitching parameters and its corresponding

Reynolds number for the test cases are shown in Table 5-2.

Table 5-2 Pitching parameters for numerical simulation image sequence

Pitching parameters (amplitude and rotational

speed)

Reynolds number

1 20 degrees; 100 degree/s 8200



5-4-2-1 Image sequences for vorticity plot of pitching flat plate with a

pitching amplitude of 20degree and rotational speed of 100deg/s (Rechord =

8200)

This section presents the vorticity plot obtained from an LES computation on a

pitching flat plate with pitching amplitude of 20 degrees and a pitching speed of

100 degree/second. The corresponding Reynolds number is 8200 (0.064 m/s).

Since the Reynolds number is the lowest among these cases and the inertial of the

flow is the least, therefore, the fluid (Figure 5-17) appears to be sticky as compared

to the rest of the test cases. Figure 5-17 shows a vortex forming at the leading edge

when the plate started to pitch down (at t = 0 T), this feature was detached from the

flat plate while the pitching angle was further increased (t = 0.25 T). When the

plate was pitched back in opposite direction (t = 0.75 T), another LEV was formed

at the bottom of the plate and shed to the down-stream. As the pitching flat plate

pitched symmetrically up and down and LEVs were subsequently formed on both

the top and bottom regions of the pitching plate, the LEV did not assist in

producing positive lift over entire pitching cycle.

Besides the above mentioned reasons, Dickinson [34] suggested that the wake

capturing, which refer to the effect of momentum transferring from the vortices to

the flapping wings at its wake region, significantly influences the performance of

the flapping wings. He further explained that the aerodynamic peak is generated

when the wing reverses its flapping direction and encounters the induced velocity

thus transferring fluid momentum to the wing. However, for symmetrical pitching

mode, the second half cycle repeats the first half cycle of pitching motion in

opposite direction. Thus, the fluid momentum transferred to the flat plate during

pitch-up and pitch-down motion neutralizes each other and causes the averaged lift

over entire cycle to become zero.

Apart from that, the symmetrical pitching plate with this set of pitching parameters

is found to be incapable of producing significant thrust as the thrust indicating

vortex street did not appear at the down-stream of the pitching flat plate from these

image sequences.

The Kármán vortex street can be observed from this set of image sequences, as

refer to t = 1.75 T, the direction of the “mushroom head” is pointing to the up-

stream where this particular feature indicates that the object is experiencing drag.

Besides the direction of the “mushroom head”, the rotational direction of vortices

at the wake region can also identified the Kármán vortex street where the top row

of vortices is rotating clockwise (blue) and the bottom row of vortices is rotating

anti-clockwise (red).

t = 0T

t = 0.25T

t = 0.5T

t = 0.75T

t = 0.85T

t = 1T

t = 1.75T


pitching amplitude of 20 deg and rotational speed of 100 deg/s in time

sequence

5-4-2-2 Image sequences for vorticity plot of pitching flat plate with a

pitching amplitude of 20degree and rotational speed of 100deg/s (Rechord =

12240)

This section presents the vorticity plot of the pitching plate with the free-stream

velocity of 0.102 m/s (Rechord = 12240). As compared to the previous section, the

inertia of the flow is higher with the Reynolds number increased. Hence, the

“stickiness” of the fluid is reduced. The amplitude of the lift peak is higher as

compared to the previous case because the increased in the fluid travelling velocity

allows higher fluid momentum to be transferred to the pitching plate. This is

analogous to a fixed wing aircraft which experiencing higher lift when it is

travelling at higher speed. As the Reynolds number is increased, the magnitude of

the vorticity (Figure 5-18) is also increased from 1.5 rad/s to 3 rad/s.

The Kármán vortex street which is shown in Figure 5-16 is almost identical to the

vortex street obtained from the previous case. As highlighted in the image

sequences, the top row of the vortices is rotating clockwise (blue) and the bottom

row of vortices is rotating anti-clockwise (red). Hence, this image sequences show

that the pitching flat plate with this particular set of pitching parameters and the

free-stream velocity was also unable to produce thrust.

t = 0T

t = 0.25T

t = 0.5T

t = 0.75T

t = 1T

t = 1.25T

t = 1.5T

t = 1.75T

t = 2T

Figure 5-18 Z-component Vorticity plots for

Reynolds number of 12240 with pitching amplitude

of 20 deg and rotational speed of 100 deg/s in time

sequence

5-4-2-3 Image sequences for vorticity plot on pitching flat plate with

a pitching amplitude of 20degree and rotational speed of 100deg/s (Rechord

= 16320)

The last set of image sequences present the vorticity plot of pitching plate with the

free-stream velocity of 0.132 m/s (Rechord = 16320). Although the averaged lift over

a cycle is still remains at zero (Figure 5-16), the peak of the lift is the highest

among Re = 8200, 12240 and 16320. The reason for the peak of lift is the highest

in this case is due to the momentum of the fluid transferred to the pitching plate is

the highest where the free-stream velocity is the highest.

However, the tiny thrust generated from the pitching motion is unable to overcome

the drag as the high free-stream is creating significant large drag on the pitching

plate. Thus, the Kármán vortex street appears again at the downstream instead of

the thrust indicating vortex street. Similarly, as circled in Figure 5-19, at the wake

of the pitching plate, the vortices at the top row are rotating in clockwise direction

and the bottom row are rotating in anti-clockwise direction.

In order to obtain a set of parameters which can successfully produce thrust or lift,

other pitching motions, such as non-symmetrical pitching, or larger pitching speed

or amplitude can also be performed across range of Reynolds number.

t = 0T

t = 0.25T

t = 0.5T

t = 0.75T

t = 1T

t = 1.25T

t = 1.5T

t = 1.75T

t = 2T

Figure 5-19 Z-component Vorticity plots for

Reynolds number of 16320 with pitching amplitude

of 20 deg and rotational speed of 100 deg/s in time

sequence

5-4-4 Conclusions on symmetrical pitching plate

The above study which was conducted on symmetrical pitching flat plate shows

that the pitching frequency, amplitude and free-stream velocities have great

influences to the flapping wings aerodynamic. At lower Reynolds numbers, higher

pitching amplitude provides a higher peak of lift. However, lower pitching

amplitude (smaller than the static stall angle), with increasing Reynolds number,

allows a higher peak value of lift to be achieved. Therefore, during the travelling of

micro UAV or UWV, the flapping parameters have to be tuned for different

travelling mode (take off, accelerate or steady speed travelling). For example, if

high thrust needed for moving forward from stationary, high pitching amplitude or

frequency is more appropriate. Besides that, high flapping frequency and amplitude

can also be utilized in hovering mode, which is similar to the hovering mode of

humming bird. If the vehicle is in steady travelling mode, lower flapping amplitude

and frequency will be recommended as it requires the least energy.

Lift and thrust play as important roles generation for micro UWV or UAV

propulsion; however, up to this section, no discovery on the symmetrical pitching

hydrofoil with the combination of pitching parameters conducted has the ability to

produce significant lift. Since the symmetrical flapping mode with the tested

parameters in the previous section is incapable of producing positive lift, to save

for the effort for investigating on more combination of flapping parameters in

symmetrical mode; the non-symmetrical pitching mode will be investigated in the

continuing quest to discover a suitable flapping mode to produce a positive

averaged lift.

In general, flapping wings kinematic which mimics animals’ motion include:

Non-symmetrical flapping motion which mimics birds or insects flight;

Symmetrical flapping motion which mimics fishes swimming.

Hence, these two categories of flapping motions have to be studied in detail

independently for the propulsion of the micro UAV or UWV.

In order to mimic birds or insects flight, the simplified kinematic motions and the

lift enhancement mechanisms which were mentioned in Chapter 2 are necessary to

be studied in order to utilize these features for improving the flapping wings

performance. For birds flying, the motions can be generally divided into two stages

[38], the down stroke (power stroke) and the upstroke (recovery stroke). During the

down stroke, the angle of attack is increased and a lot of kinematic motions were

involved by the bird in order to provide massive thrust and lift. The wing was

twisted and allow varies of the angle of attack to be appeared along its wingspan.

During the up stroke, the bird will fold its wings inward to further reduce the

upward resistance and also reduce the angle of attack during this stage for

optimizing the total lift.

However, complicated kinematic motions require a numbers of actuators to

perform the motions as mentioned above, and these extra actuators will further

increase the size of micro vehicle. Therefore, in the next study, these motions were

simplified as non-symmetrical pitching and were investigated for its capable to

retain the lift enhancement mechanism so as to obtain a set of flapping motion

which can produce greater positive lift.

In contrary, it is noted that fishes are employing symmetrical pitching of flexible

tail to produce thrust for moving forward; as discussed in Chapter 2, Triantafyllou

[59] and Dickinson [60] discovered that oscillating hydrofoil in symmetrical mode

which simulating the swimming motion of fishes can generate a significant positive

thrust. Hence, together with the above factors, the flexibility of fish tail which flap

symmetrically has inspired the author to conduct set of experiments on pitching

rigid base hydrofoil and pitching hydrofoil with chord-wise flexible extension with

fixed pitching parameters to investigate the relationship between the flexibility of

the hydrofoil to the thrust. Therefore, the following section discusses the effect of

the chord-wise flexibility of the pitching hydrofoil to the thrust performance. In

addition, the combined heave and pitch motion was also studied for investigating

the effect of phase different between pitch and heave to the thrust. This particular

study will be discussed after the following section.

5-5 Thrust indicating Vortex Street from a symmetrical pitching

hydrofoil

Figure 5-20 SD8020 (span width of 0.32m and chord length of 0.12m) with

flexible trailing edge extension

Figure 5-20 shows the dimensions of the flexible trailing edge extension and Figure

5-21 presents the snapshot from dye flow visualization which was conducted on the

pitching rigid foil with and without the 60 mm flexible chord-wise extension at its

trailing edge. The force measurements results on pitching rigid hydrofoil, with 60

mm and 120 mm are plotted in Figure 5-24 and Figure 5-25. The purpose of

conducting the dye flow visualization is to observe the presence of the Reverse

Kármán vortex street as well as to investigate the effect of chord-wise flexibility to

the thrust. The dimensions and the pitching parameters for this particular hydrofoil

are summarised as below:

Hydrofoil profile: SD 8020

Chord-length: 120 mm

Span-width: 320 mm

120 mm

60 mm

60 mm

Pitching amplitude: 40 degrees

Pitching speed: 0.87 rad/s (50 degree/s).

Pivot point: Quarter chord

The trailing edge extension is made from the cellulose acetate, which has a density

of 1.3g/cm3 and refractive index of 1.49. It has a tensile strength of 12 to 110 MPa

and tensile modulus of 1.0 to 4.0 GPa. The commercial cellulose acetate is made

from processed wood pulp which is processed using acetic anhydride to form

acetate flake. [61] & [62].

From Figure 5-21a, the reversed Kármán vortex street cannot be observed from the

pitching rigid hydrofoil without the flexible extension. However, after the flexible

trailing edge extension was attached to the hydrofoil and pitched with the same

pitching parameters, a strong reversed Kármán vortex street can be clearly

observed at the wake (Figure 5-21b) and shed to the downstream. This set of

reversed Kármán vortex street can be identified by the mushroom head with the

arrows pointing to the downstream, as shown in Figure 5-21b.

Figure 5-21 SD8020 (a) without and (b) with flexible trailing edge extension

for Dye Flow Visualization at U=0.1028m/s, θ=40o and w=0.873rad/s

To find out the capability of flexible trailing edge extension for generating thrust,

apart from dye flow visualization, direct force measurement was also conducted. In

addition, the myth about the reversed Kármán vortex street as a thrust indicating

vortex street can be verified as well. In this test, the selected pitching amplitudes

are 30 degrees and 40 degrees; the pitching speed is fixed at 50 degree per second.

In order to measure the pure thrust without the contribution of the drag from the

free-stream, these set of measurements were conducted at zero free-stream velocity.

As a reflection from the dye flow visualization, the measured thrust from the

pitching hydrofoil with the flexible extension is indeed higher than pitching rigid

hydrofoil. As shown in Figure 5-24 and Figure 5-25, the thrust generated by the

a)

b)

pitching hydrofoil with the flexible extension is almost doubled compare to the

measured thrust from pitching foil without the extension. However, the length of

the trailing edge extension (6 cm or 12 cm) did not have significant influences to

the generated thrust.

The hybrid of rigid base hydrofoil and the flexible extension at the trailing edge

allows the pitching hydrofoil for utilizing the momentum transferred from the fluid

and produced a higher thrust where the elasticity of the flexible extension plays an

important role for it.

Before the discussion on how the flexible extension able to enhance the thrust, the

capability of pitching rigid hydrofoil to generate thrust can be explained as below:

When the hydrofoil is started to pitch from its origin (Figure 5-22a); the pitching

hydrofoil will “carry” the fluid around the bottom side of the hydrofoil to travel in

the same direction with the pitching motion. Once the hydrofoil has pitched to its

maximum amplitude and pitched back instantaneously, the hydrofoil is

experiencing both the reaction force from the fluid (due to the current pitch back

motion, and it is opposite to the pitching direction) as well as the “remaining” fluid

momentum which has been “carried” by the previous motion (Figure 5-22c). Hence,

this increases the resultant force experienced by the hydrofoil and the peak of the

thrust is produced at this instance.

t = 0s, the hydrofoil start to pitch

t < 1/4T, the hydrofoil is pitching

to the maximum pitching

amplitude

t = 1/4T, at maximum pitching

amplitude. The hydrofoil stops and

pitches in reversed direction

instantaneously

Figure 5-22 Illustration on the thrust and pitching motions

FReaction

ω “remaining” fluid from

previous motion

ω

a)

b)

c) Thrust

V1

Reaction force from the fluid due

to the pitching motion, ω

Wake region

Fluid at the bottom of

hydrofoil which is “carried”

by the pitching hydrofoil and

travels in the same direction

with the pitching motion

Figure 5-23 Resultant forces acting on the pitching hydrofoil (a) without and

(b) with flexible extension

As mentioned previously, the elasticity of the flexible trailing edge extension plays

an important role for enhancing the thrust. With suitable degree of elasticity, when

the pitching hydrofoil was pitching at the reversed direction (at t = ¼ T)

instantaneously, the flexible extension are able to sustain the reaction force

(contributed by the back pitching motion) and the “remaining” fluid momentum

from the previous pitching motion more effectively; if this flexible extension is

rigid enough and yet can be bent to resolved the resultant force vector more

towards to the direction of thrust as compared to pitching of rigid hydrofoil (Figure

5-23), a higher thrust can be achieved. As a conclusion, the elasticity of the

Fresultant

FThrust

FLift

FThrust

FLift

Fresultant

a)

b)

pitching hydrofoil could greatly improve the thrust. Therefore, it is suggested that

more force measurements can be conducted on various combinations of flapping

mode and different degree of flexibility of the hydrofoil with higher accuracy force

transducer in order to obtain set of optimized parameters and the flexibility

constant for producing higher lift, thrust and improve the propulsive efficiency for

the flapping micro UAVs and UWVs.

Figure 5-24 Time history thrust with Pitching amplitude: 30deg; Pitching

speed: 50deg/s

Figure 5-25 Time history thrust with Pitching amplitude: 40deg; Pitching

speed: 50deg/s

5-6 Thrust from symmetrical heave and pitch SD8020 (In phase and 180 degrees out of phase)

Besides solely heaving or pitching motions, combination of these motions can

mimic the fish swimming motion even closer [6]. Although micro fish-like vehicle

might face the limitation of size and should avoid using extra actuators, the larger

size UWV might be able to employed combined pitch and heave motion for

propulsion in order to generate greater thrust. However, the phase different

between pitch and heave motion has significant effect to the performance of thrust.

Hence, this section reveals the influences of the phase different (in-phase or 180

degrees out of phase) to the thrust generated by the hydrofoil SD8020 (same

hydrofoil as previous section) in combined heave and pitch motion. In order to

investigate only the effect of phase different, the hydrofoil was moved with

different phase angle but keeping the same pitching and heaving parameters across

these two tests. The parameters are as below:

Pitching amplitude : 40deg

Pitching speed : 84 deg/s

Heaving amplitude : 10 mm

Heaving speed : 0.021m/s

Figure 5-26 Combined heave and pitch motion – in phase

Figure 5-27 Combined heave and pitch motion – 180 degrees out of phase

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1

t/T

Am

pli

ud

e

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1

t/T

dis

pla

cem

en

t

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1

t/T

an

gle

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1

t/T

dis

pla

cem

en

t

c)

a) b)

a) b)

c)

Figure 5-28 Experimental setup for combined heave and pitch study

Figure 5-26c illustrates the motion of SD8020 which is undergoing the pitching

and heaving motion with in phase mode and Figure 5-27c illustrates the motion of

SD8020 with 180 degrees out of phase mode.

The in-phase mode can be defined as:

The hydrofoil is pitch and heaves to the same positive direction and goes back to

the origin in synchronized motion profile.

The 180 degrees out of phase mode can be defined as:

The hydrofoil is heaved to the positive direction but pitched to the negative

direction at the beginning and go back to origin from different direction.

The individual heave and pitch motion of the hydrofoil are further illustrated in

Figure 5-26 and Figure 5-27 (a & b). The experiment setup for this study is shown

in Figure 5-28. The Cool muscle high resolution closed loop stepper motor was

employed for generating the pitching motion, while the THK linear guide and the

slider were responsible for the heaving motion.

The dimensions of the hydrofoil are stated as below:

Hydrofoil profile SD 8020

Chord-length : 120 mm

Span-width : 320 mm

Pivoting point : Quarter Chord

The results from the instantaneous force measurement are shown in Figure 5-29

and Figure 5-30. By comparing the peak of the thrust curve from both cases, in-

phase motion has a higher peak than the out-of-phase motion (180 degrees) by 50%

(approximately increased by 0.75N) despite the motions and flapping parameters

across these two cases are fixed.

Figure 5-29 Time history thrust by combined motion with in phase mode

Figure 5-30 Time history thrust by combined motion with 180 degrees out of

phase mode

The main reason for the in-phase mode to obtain higher thrust might due to this

particular flapping mode is able to capture the momentum transferred from the

fluid which is contributed by the flapping motion more effectively.

In this mode, the hydrofoil was heaved and pitched to the same direction at the

beginning. The fluid at the wake region of the flapper is “following” the moving

hydrofoil. At this particular moment, the fluid that was “following” or being “bring”

by the hydrofoil started to build up its momentum. When the hydrofoil is moving

back to its opposite direction instantaneously at the quarter cycle (in phase), the

thrust reaches its thrust peak as the total resultant force is not only from the force

introduced by the current flapping motions and also include the momentum of the

fluid transferred to the hydrofoil, which was created by the previous motion.

However, for the 180 out of phase motion, as the pitching and heaving motion are

opposing to each other at the beginning, the momentum of the fluid that “following”

the hydrofoil at the wake was reduced. At the quarter cycle, the hydrofoil was

moved back to the origin with heave and pitch motion from different direction. At

this moment, the peak of thrust occurs, but with the reduced momentum of fluid

from the previous motion.

As a conclusion, this set of experiment shows that the phase difference between the

heave and pitch motion is important for the wake capturing [23] ability. Hence, in

order to obtain higher thrust for the UWV, the proper motion parameters and the

phase angle have to be carefully tuned.

5-7 Investigation of LEV with Non-symmetrical Pitching Motion

As discussed in Chapter 2, many researchers have conducted series of experiments

for investigating the ability of LEV to enhance the lift on combined heaving and

pitching of hydrofoil in non-symmetrical mode. However, motions with more

degree of freedoms involved will necessitate additional actuators. The limitation on

the size of the micro UAV requires the design of the flapping wings mechanism to

be as simple as possible. Hence, this section discusses the study on simplified non-

symmetrical pitching only motion in a very slow free-stream, which mimics the

birds’ motion in the beginning of flight. The kinematic pitching motion for this

study can be described as a pitch down, hold and pitch back motion. The hydrofoil

used is with SD7003 profile. The dimensionless pitch rate ( ) and dimensionless

time are defined in Equations 5-7 and 5-8:

(5-7)

(5-8)

where Ω is the pitching speed (rad/s), U is the free-stream velocity (m/s) and c is

the chord-length of the hydrofoil.

The experiment was conducted in a closed-loop water tunnel; a six-axis force

transducer (ATI gamma

SI-32-2.5) was used for the force measurements. Dye

flow visualizations were also conducted to investigate the flow structure and verify

the influence on lift by the following factors: free-stream velocity, pitching speed,

hold time under linear pitching motion as well as the formation of LEV (leading

edge vortex).

A high resolution stepper motor (Cool muscle

motor CM1, tuned to 12,000 pulses

per revolution) was used to generate the motion with the input parameters from a

computer. The flow condition is Rechord = 1 x 104 (0.085m/s of free-stream velocity

at the test section of the water tunnel) and the dimensionless pitch rates (Ω+) of 0.2

and 1.4 were applied. A comparison of the the Cl curve with the dye flow

visualization for every time increment will be presented in this section. The

formation and detachment of the LEV and the dynamic stall effect were observed in

this experiment.

The flapper is a SD 7003 hydrofoil which made from aluminium alloy Al 6061

with carbon coated surface. It has a span-width of 400 mm and a chord-length of

120 mm. The hydrofoil is pivoted at the quarter chord from the leading edge which

has a maximum thickness of 10 mm. (refer to Figure 5-32). The experiment setup

is shown in Figure 5-33. The non-symmetrical pitching motion and the flow

conditions are illustrated in Figure 5-34. For ease of presentation and comparison

of results to the other research group, the results were converted into dimensionless

terms.

The motion parameters and dimension of the hydrofoil are as below:

Hydrofoil profile SD 7003

Chord-length 120 mm

Span-width 400 mm

Pivoting point Quarter Chord

Figure 5-31 Cross-sectional profile of SD 7003 hydrofoil [58]

Figure 5-32 CAD drawing of SD7003 hydrofoil

Figure 5-33 Experimental setup

Figure 5-34 Pitch up, hold and pitch down motion

As mentioned, the hydrofoil was undergoing pitch down, hold and pitch back

motion. The hydrofoil was pitched to the maximum angle of 40 degree (beyond the

static stall angle of attack) and pitched back after a holding time of thold/t+ equal to

0.05 and 1.00 respectively in two pitching motion pattern, i.e. linear sudden

pitching and smooth gradual pitching (Figure 5-34).

The experiment was conducted to investigate the effect of the angular velocity

(ramp rates) and the acceleration (torque) caused by a rapid pitch down motion to

the lift, i.e the Kramer effect. The angular position, angular velocities and

acceleration versus t/t+ for both pitching patterns are shown in Figure 5-35 and

Figure 5-36 (the holding time was kept at thold/t+ = 0.05 for both linear sudden

pitching and smooth gradual pitching patterns).

The linear sudden pitching pattern allows the hydrofoil to experience sudden start

and stop motion with the angular acceleration of 800 deg/s2 (for the case of Ω

+ =

0.2); whereas, the angular acceleration for the smooth motion is only 30 deg/s2. For

the linear pitching pattern, the angular velocity was kept constant throughout the

pitching motion for linear. In contrast, the angular velocity increases in magnitude

with time (constant ramp rate) for the smooth pitching pattern.

The force measurements were also being conducted to investigate the effects of

rotational speed (in terms of the dimensionless pitch rate, Ω+) and the pitch rate

(sudden pitch-delta function type pitching rate or smooth gradual pitching-linear

function type pitching rate) to the lift. The force measurement results of are shown

in Figure 5-37 and Figure 5-38.

The lift coefficients obtained from linear sudden motion with higher pitch rate are

generally higher than that of smooth motion with higher pitch rate by

approximately 20% as the acceleration and deceleration of the motion profiles are

more significant for high pitch rate than low pitch rate (as circled in Figure 5-35

and Figure 5-36). The larger lift experience by higher pitch rate with sudden

motion is caused by the torque required to produce such motion as it requires a

large acceleration or deceleration (angular acceleration ~ 800 deg/s2) whereas the

gradual motion needs only a small fraction of the sudden motion (angular

acceleration ~ 30 deg/s2). In other words, the difference arises from the fact that a

slowly increasing speed (instead of sudden motion) experiences less reaction force

from the surrounding fluid. Hence, less lift force is produced.

Figure 5-35 Motion profile of the non-symmetrical pitching motion (Ω+ =

0.2)

Figure 5-36 Motion profile of the non-symmetrical pitching motion (Ω+ =

1.4)

Figure 5-37 Lift coefficient Vs dimensionless time with linear sudden motion


+ =1.4;

hold time 0.072sec (left) and 1.4 sec (right)

Averaged CL = 0.79 Averaged CL = 0.84


Figure 5-38 Lift coefficient Vs dimensionless time with smooth motion


+ =1.4;

hold time 0.072sec (left) and 1.4 sec (right)



Figure 5-38 shows that the Cl curve peak (represented in green) is coinciding

closely with the angular position curve (represented in blue) for smooth pitching

motion. On the other hand, the Cl curve peak does not follow the position of the

angular position curve closely in Figure 5-37, especially at high pitch rate; this is

because the ramp-up acceleration is greater. The sudden pitch up motion allows the

hydrofoil to move faster than the rate that the surrounding fluid could ‘sense’ or in

a proper word, response or settle in time. The shift in the Cl curve peak and sudden

pitch up at the start, means that the surrounding fluid cannot respond in time and

lags behind the motion of hydrofoil. At the end of the pitch up and down cycle, the

Cl curve has a negative gradient, which follows the trends in the angular position

curve.

Similarly, for the gradual pitch motion, the hydrofoil moves slowly enough to

allow the surrounding fluid to ‘sense’ and respond before the motion completes.

The gradual pitch up at the start allows sufficient time for the surrounding fluid to

settle. One of these manifestations is the formation of leading edge vortex as shown

in the dye flow visualization in Figure 5-39 and Figure 5-40. At the end of the

pitching motion, the Cl curve reverses its trend and regains its positive gradient

whereas the angular position curve still has a negative gradient. The upwards

gradient is due to the flow reattachment prior to the completion of pitch-down

motion.

The hold time influences the averaged lift over entire pitching significantly, but it

appears to have no impact on Cl, during the beginning of pitching, therefore, the Cl

profile is similar in the first half of the cycle. The longer hold time allows the flow

to reattach back to the airfoil. Hence, the recovery of Cl at later half cycle then

results in a higher averaged lift in total cycle.

In term of magnitude of peak lift, higher pitch rate (Ω+ =1.4) in sudden pitching

motion can produces greater peak lift. Cl peak of linear-sudden motion is 2.75 and

Cl peak for smooth motion is 2.25. However, also at higher pitch rate, the averaged

lift for linear sudden motion (0.77) is lower than the smooth motion (1.02) for short

holding time (hold time = 0.072s), although linear sudden motion has a slightly

higher peak lift. Next, for similar motions with longer hold time (hold time = 1.4s),

the averaged lift is increased from 1.47 to 1.85. The above cases show that the LEV

is allowed to stay above the hydrofoil with a longer holding time. In addition, when

the hydrofoil is started to pitch back, the re-attachment of LEV allows the

increment of the total averaged lift.

The following section compares the images sequence which obtained from dye

flow visualization (Ω+ = 0.2, hold time of 0.072sec and free-stream velocity of

0.085m/s) and to the results from the direct force measurement. The purpose of this

particular study is to investigate the influences of the LEV to the lift. The averaged

lift coefficients for the above cases are tabulated in Table 5-3 and Table 5-4.

Table 5-3 Averaged lift coefficient over entire pitching cycle (Linear

sudden motion)

hold time = 0.072s hold time = 1.4s

Ω+ = 0.2 0.79 0.84

Ω+ =1.4 0.77 1.85

Table 5-4 Averaged lift coefficient over entire pitching cycle (Smooth

motion)

hold time = 0.072s hold time = 1.4s

Ω+ = 0.2 0.65 0.72

Ω+ =1.4 1.02 1.47



vortex (LEV) forming



vortex (LEV) forming (cont.)

Figure 5-41 Lift and position curve for Ω

+ = 0.2, hold time of 0.072sec and

free-stream velocity of 0.085m/s (corresponding to the dye flow visualization)

The formation and the “bursting” of the LEV can be clearly observed from the dye

flow visualization images sequence. Many researchers, for examples, Tani (1964)

[63], Carmicheal (1981) [64], Ellington (1984) [65] and also Shyy (2008) [34],

have described the LEV as an enhanced lifting mechanism for sustaining the lift for

flapping flight.

In Figure 5-40 (when t/t+ = 0), the hydrofoil is at its original position and the flow

passing the hydrofoil stays attached. However, when the foil begins to pitch, flow

separation can be clearly observed and a “bubble” [66] (flow reversal) starts to

form at the leading edge (at t/t+ = 0.866) and grows in size. As the LEV continue

growing, the lift is able to sustain even the hydrofoil is beyond the static stall angle

of attack, causing the delayed stall to occur.

When the hydrofoil had reached the maximum pitching amplitude of 40 degrees, it

was held stationary for 0.072 sec. The holding also allows the momentum of the

fluid from the previous down-pitching motion to dissipate and reduced the

downward force experience by the hydrofoil. At this moment (holding stage),

where the AOA was at 40 degrees, the LEV is separated from the hydrofoil with

large separation and the lift was dropped tremendously (Figure 5-41). During the

“holding” stage, the LEV was grew in size and shed to the upper side of the

hydrofoil. Therefore, the flow over the LEV was slightly accelerated and retained

the lift slightly. As the hydrofoil started to pitch back, the LEV was further re-

attach back to the upper surface of the hydrofoil for a short moment (at t/t+

= 4)

before the LEV was fully shed away from the hydrofoil. Hence, the drop of the lift

was sustained. At t/t+

= 5 and beyond, Figure 5-41 shows that the lift drop

tremendously and the corresponding image from dye flow visualization shows the

LEV was shed to the trailing edge and separated or expelled from the hydrofoil.

Explanation for higher pitch rate with short holding time cannot obtain higher

averaged lift is as below:

The LEV, in this case, might be expelled and separated from the hydrofoil instantly

during the pitching back motion. Therefore, the LEV was unable to assist the rapid

pitching hydrofoil for increasing the averaged lift over entire pitching cycle (Figure

5-37 and Figure 5-38).

In conclusion, the lift charts (Figure 5-37 and Figure 5-38) from this section shows

that non-symmetrical pitching motion can successfully produce a positive averaged

lift over the entire pitching cycle.

The findings of this section on non-symmetrical pitching mode can be summarised

as follows:

Non-symmetrical motion, with pitching only at one side (simplified bird

flapping motion); it can prevent the cancelation of the lift from the

downward force created by the pitching motion at another side.

Due to this half-cycle (non-symmetrical) pitching motion, the LEV was not

formed at the bottom side of the pitching foil. Therefore, the LEV was able

to enhance the lift significantly.

In general, rapid rotation of the hydrofoil allows higher aerodynamic lift

peak to occur, however, the holding time decides the magnitude of the

averaged lift.

Control of the duration of LEV for staying over the hydrofoil, by

optimizing the hold time between down-stroke and up-stroke, combined

with optimized flapping parameters, can significantly improve the lift

performance.

Extremely long holding time is not advisable for large pitching amplitude

which is beyond the static stall angle of attack as the lift might drop

abruptly once the effect of the LEV is diminished.

Chapter 6 Analytical Model for the

Prediction of Peak Lift of a Pitching Plate

The aerodynamics of flapping wings is very hard to predict due to its non-linearity,

unsteadiness of the flow and complex kinematic motions involved. Therefore, Liu

(Liu, 2007) and Kang (Kang, Aono, Trizila, Baik, Michael, & Shyy, 2009) [20] &

[37] concluded that, in order to predict flapping wing aerodynamics accurately, the

only technique is to solve the unsteady Navier stoke equation.

However, conducting extensive computational or experimental studies are costly

and time consuming. Hence, from the experimental and numerical simulation data

obtained in this thesis, a simple prediction model, which can predict the peak lift

coefficient from pitching flat plate, can be derived.

Such a model aims to aid during the preliminary design stage of an MAV or UWV

and can be used for optimization, before more extensive computational and

experimental studies are performed.

6-1 Derivation of Analytical model

As discussed from the previous chapter, the pitching motion affects the lift and

thrust significantly. Hence, this thesis aims to develop a simple analytical model

which is in the form as below:

(6-1)

It has been shown, that a quasi-static analysis, which approximates the

instantaneous forces acting on the flapping wings by calculating the steady forces

during the steady motion at identical free-stream and angle of attack is insufficient

to predict the peak and the mean lift (Elington, 1984) [65]. Kramer [18] discovered

that, besides the contribution of lift due to LEV, the wing could achieve higher lift

due to rapid wing rotation and delayed stall. Hence, this current analytical model is

being developed based on the combination of lifting line theory [67] and the

Kramer effect. The derivation of the total lift (L) from the any airfoil can be

expressed as:

(6-2)

The total lift coefficient ( can be hence represented by:

(6-3)

(6-4)

(6-5)

Following thin airfoil theory, the lift coefficient for the lift due to the angle of

attack (AOA) can be simplified as:

(6-6)

where the AOA, , is in radian. This expression neglects stall effects. However,

due to the effect that delayed stall is observed (see Kramer and the previous

chapter), for the sake of simplicity stall is not considered. The implications are

discussed below in the results section.

Next, the circulation due to the rotational speed of the pitching plate can

be derived by as:

(6-7)

(6-8)

Hence, the lift coefficient due to the pitching motion becomes:

(6-9)

Hence, total lift coefficient as is computed in the current model as:

(6-10)

where the angle of attack , and the rotation rate are time dependent.

6-2 Results from analytical model

The following section presents the estimated lift coefficient from the pitching flat

plate by the derived model and its outcomes are compared with the experimental

and numerical simulation results. The parameters used for comparison are the test

cases that use a pure pitching movement and are summarised as below:

Table 6-1 Pitching parameters and Reynolds number

Reynolds number Pitching amplitude

(degrees)

Pitching speed

(degrees per second)

19200 20 50

19200 40 100

8200,12240,16320,19200 20 100

The estimated total lift coefficient from Equation (6-10) consists of two

components; first, the lift due to the free-stream acting on the flat plate at particular

instant angle of attack (AOA) and second, the lift due to the rotational motion of

the pitching flat plate.

The described motion of the symmetrical pitching flat plate (Figure 6-1) for the

prediction model was saw tooth motion, and it can be described as; first, rotate in

clock-wise direction to the maximum pitching amplitude in constant speed. Second,

rotate counter clock-wise to the maximum pitching amplitude at the other direction

and finally rotate clock-wise again and back to the origin (0 degree) with a constant

speed as well

Figure 6-1 Symmetrical pitching motions of flat plate

Figure 6-2 Results from pitching flat plate with pitching parameters of 20 deg

50 deg/s (Left) and 40 deg 100 deg/s (right) with fixed Reynolds number of

19200

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1

t/T

Am

pli

ud

e

Firstly, the results are compared with the fixed Reynolds number of 19200 across

the pitching amplitude of 20 and 40 degrees corresponding to the pitching speed of

50 and 100 degrees per second respectively in order to validate its ability for

estimating the lift coefficient across different pitching parameters (Figure 6-2). It

can be seen that this model has quite considerable overall differences in shape. This

is to be expected, as the model cannot capture complex effects as the LEV.

However, the model is able to predict the peak lift coefficient with considerably

accuracy. At its peaks, the model matches well with the experimental and

computational results.

Figure 6-3 elaborates further on the differences between model and experimental

and computational results. At the beginning of the pitching cycle (t=0), the

rotational speed is fixed and the starting lift coefficient is solely contributed by the

first term of Equation 6-10, the lift due to the rotational motion of the flat plate. As

the angle of attack increases, the lift due to the angle-of-attack increases and the

overall lift increases as well. During the pitch-up motion the model agrees

reasonably well with computational and experimental results. As the pitching

motion reverses the model predicts a drastically lower lift, as the circulation due to

the rotation introduces now negative lift. The computational results show that in

that period of time the LEV passes over the upper side of the plate. As the present

model cannot capture this non-linear effect, the differences between model and the

current experimental and numerical results are particularly high. The second

maximum peak, however, is well predicted in size and timing.

Figure 6-3 Ilustration of predicted lift components (green dotted line)

Lift due to LEV

Predicted total lift (green dotted line)

Pitching motion

CL due to rotation motion

CL due to instantaneous AOA

+

==

Re =8200

Re = 12240

Re=16320

Re=19200

Figure 6-4 Results from pitching flat plate with fixed pitching parameters

(20 degrees and 100 degrees per second) across Reynolds numbers of 8200,

12240, 16320, 19200

Next, to determine the ability of the model to capture the effect of Reynolds

number, the predicted results are compared with the experimental and numerical

simulation results as well in the fixed pitching parameters of 20 degrees and 100

degrees per second across the Reynolds of 8200, 12240, 16320 and 19200

respectively (Figure 6-4). As the model is derived from simple mathematical

models, the effect of viscosity is neglected (or modelled through the introduction of

the circulation, ). The results show the same trend as previously observed: While

the temporal lift prediction is not well predicted, especially after the apex of the

pitching motion has been achieved, the peak lift is predicted reasonably well. In

particular, the peak lift prediction has a larger error at low Reynolds-number,

which can be explained by the effects of viscosity.

6-3 Conclusion of analytical model

This chapter, a model to predict the lift distribution of a pitching plate has been

derived. Although this particular analytical model is not able predict the temporal

lift curve as compared to the results from the experimental and numerical

simulation approaches, this model can still be employed for the preliminary study

of flapping wings for estimating the peak lift.

Chapter 7 Conclusion and

Recommendations

In this chapter, key findings on the conducted research works are summarized.

Future developments and possible improvements for studying and optimizing the

flapping wings aerodynamics performance are also presented.

7.1 Summary

From the past reviews, the study of flapping wings aerodynamics was found to be

extremely challenging due to the unsteadiness of flow and the complicated

kinematic motions involved from the flapping wings. In recent year, Platezer [17]

and Guerrero [38] also stated that the study and application of flapping wings still

remains open and the physics of the flapping wings aerodynamics are yet to be

fully understood. Due to foregoing, this thesis investigated the feasibility of the

flapping wings with simplified kinematic motion as propulsion unit for micro

vehicles by studied the aerodynamics of the flapping wings at low Reynolds

number through experiment (force measurement and dye flow visualization) and

numerical simulation. The lift and thrust enhancement mechanisms, and the

affecting parameters to the aerodynamic performance of flapping wings were also

being investigated in detail in order to serve as database for optimizing the

performance of flapping wings.

Measuring of small dynamic forces which generated by the flapping wing motion

is challenging. Therefore, a test rig, which has the capability to produce the

kinematic motions and to measure the forces, was carefully designed and

developed. The capability of novel Immersed Boundary LES solver code has also

been evaluated for simulating flapping wing aerodynamics. In addition, to reduce

the works needed for optimizing the performance of flapping wings by filtering the

flapping parameters which are generating insignificant lift, a simple analytical

model (based on Kramer effect) for predicting the peak lift was developed with the

aid from the collected experimental and numerical simulations data.

In summary, with all the conducted works which presented in Chapter 5 and 6, this

study demonstrated the factors for enhancing the lift and thrust and further revealed

the hidden myth behinds the flapping wings aerodynamics which could lead to

optimize the performance of micro UAV or UWV. Finally, the overarching goal

for translating of knowledge from the flapping wings dynamics to the development

of flapping wings micro UAV and UWV can be achieved.

7.2 Recommendation and future research

Apart from the findings mentioned in the previous section, recommendations on

equipment upgrades and further improvement could be made for flapping wings

study are listed as below.

First, in order to further reduce the size of these miniature vehicles, another

type of actuator, for example, piezoelectric or smart materials that can

provide simple motion might be able to replace the motor for generating the

simple pitching or heaving motion. The effect of the flexibility of the

chord-wise extension to the thrust can be further investigated with more

materials in different stiffness. Additionally, smart material, which can

achieved higher stiffness during the down stroke and lower stiffness during

the upstroke for re-capturing the momentum of the fluid generated by the

flapping motion, could be developed.

Second, evaluation of the capability of current solver for predicting thrust

generated by flapping wings and improvement also can be made for

simulating flexible flapping wings. Hence, with these capabilities, current

solver can serve as a good tool for optimizing the performance of flapping

wings aerodynamics.

Third, the developed simple analytical model can be further improved in

order to obtain better accuracy results as well as to capture the effects by

the LEV and other factors which could affect the lift.

Fourth, a high speed and resolution video camera can be utilized for

conducting the flow visualization in order to obtain better quality and

clearer images for observing the important mechanisms in detail.

Finally, for quantitative unsteady flow measurements, Particle Image

Velocimetry (PIV) with higher pulse rate and larger laser sheet also can be

introduced. Hot-wire measurements at the down-stream of the flapping

wing can also be an alternative approach for measuring the flow dynamics

in the wake of a flapping wing, however, here the spatial correlation of

turbulent quantities would be lost as measurements are limited to a single

point.

Ultimately, the study of flapping wings is a new era of technology and

improvements made to miniature UAV and UWV propulsion system will

contribute greatly to the future development of autonomous unmanned vehicles

which can perform important tasks as mentioned in Chapter 1.

Figure 7-1 Hummingbird micro UAV [68], robotic fish [69] and finger tip

size micro UAV [12]

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APPENDIX I Load cell/ Force transducer

Dimensions and Drawing

APPENDIX II ATI Calibration Report

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